Electric Shocks

Wenner's four-electrode method measures the average resistivity of soil by passing current between two outer electrodes and measuring the voltage between two inner electrodes, all equally spaced in a straight line. It removes the effect of electrode contact resistance.

Arrangement

Four electrodes C1, P1, P2, C2 are driven in a straight line at equal spacing $a$, to a small depth $b$ ($b \ll a$, usually $b < a/20$). A current $I$ is passed through the outer (current) electrodes C1 and C2 from an earth tester, and the voltage $V$ between the inner (potential) electrodes P1 and P2 is measured.

        Earth tester (megger)
     +---I----------------------+
     |      +---V---+           |
     |      |       |           |
     C1     P1      P2          C2
  ---|------|-------|-----------|--- ground
     |<--a->|<--a-->|<----a---->|
     depth b (b << a)

Derivation

Treat each electrode as a point source of current at the surface. Current $I$ from a point spreads into the earth over hemispheres. At distance $r$ the current density and field are

$$J = \frac{I}{2\pi r^2}, \qquad E = \rho J = \frac{\rho I}{2\pi r^2}$$

so the potential at distance $r$ is

$$V(r) = \int_r^\infty E\,dr = \frac{\rho I}{2\pi r}$$

Current $+I$ enters at C1 and $-I$ leaves at C2. Using superposition:

Potential at P1 (distance $a$ from C1, $2a$ from C2):

$$V_{P1} = \frac{\rho I}{2\pi}\left(\frac{1}{a} - \frac{1}{2a}\right) = \frac{\rho I}{4\pi a}$$

Potential at P2 (distance $2a$ from C1, $a$ from C2):

$$V_{P2} = \frac{\rho I}{2\pi}\left(\frac{1}{2a} - \frac{1}{a}\right) = -\frac{\rho I}{4\pi a}$$

Voltage between P1 and P2:

$$V = V_{P1} - V_{P2} = \frac{\rho I}{2\pi a}$$

The tester reads $R = V/I$, so

$$\rho = 2\pi a R$$

with $\rho$ in $\Omega\text{-m}$, $a$ in m and $R$ in $\Omega$.

If the electrode depth $b$ is not small compared with $a$ (image of each electrode taken), the general relation is

$$\rho = \frac{4\pi a R}{1 + \dfrac{2a}{\sqrt{a^2+4b^2}} - \dfrac{a}{\sqrt{a^2+b^2}}}$$

which reduces to $\rho = 2\pi aR$ when $b \ll a$.

Procedure and notes

• Readings are taken at several spacings ($a$ = 1, 2, 5, 10 m …) and in different directions. The current spreads roughly to a depth equal to $a$, so the change of $\rho$ with $a$ shows layered soil.
• Measurements are made in dry season to get the worst (highest) value for earthing design.
• An AC or reversing-DC tester is used to avoid polarisation and stray currents.

Example: with $a = 5$ m and $R = 3.2\ \Omega$, $\rho = 2\pi \times 5 \times 3.2 = 100.5\ \Omega\text{-m}$.

An electric shock is the physiological reaction of the body when electric current passes through it. The damage depends mainly on the current (not voltage), its path, duration and frequency.

Physiological effects (50/60 Hz, hand to feet, typical values)

Other effects: burns at entry and exit points, internal burns, damage to nervous system, fall from height due to reflex action, and later kidney damage.

Dalziel's relation for the fibrillation threshold (used in IEEE 80):

$$I_b = \frac{0.116}{\sqrt{t}}\ \text{A (50 kg person)}, \qquad I_b = \frac{0.157}{\sqrt{t}}\ \text{A (70 kg)}$$

where $t$ is shock duration in seconds (0.03–3 s).

Good safety practices to avoid shock

1. Proper earthing of all metal frames and enclosures, with low earth resistance, so a fault trips the protection quickly.
2. Use of RCD/ELCB (30 mA) and fast protective relays/fuses.
3. Isolation and lock-out/tag-out: switch off, lock, tag and test for "dead" before work; earth the conductors being worked on.
4. Insulation: use double-insulated tools, insulated mats, rubber gloves and boots of proper voltage rating.
5. Safe clearances and barriers around live parts; warning signs.
6. Substation design: earth mat, surface layer of crushed gravel, and equipotential bonding to keep step and touch potentials within safe limits.
7. Trained and authorised persons only; work permits for HV work.
8. Avoid moisture: do not touch switches with wet hands; use weather-proof fittings.
9. Regular inspection and testing of insulation, earthing and protective devices.
10. First aid knowledge: cut the supply, separate the victim with a dry insulating object, and give CPR.

The three common footing electrodes are a hemisphere, a single driven rod and a counterpoise (buried horizontal wire). Their resistances (Begamudre, EHV AC Transmission Engineering) are:

$$\begin{aligned} \text{Hemisphere (radius } r):\quad & R = \frac{\rho}{2\pi r} \\ \text{Driven rod (length } L, \text{radius } a):\quad & R = \frac{\rho}{2\pi L}\ln\frac{2L}{a} \\ \text{Counterpoise (length } L, \text{depth } y):\quad & R = \frac{\rho}{\pi L}\left[\ln\frac{2L}{\sqrt{2ay}} - 1\right] \end{aligned}$$

Given: $R = 20\ \Omega$, $\rho = 100\ \Omega\text{-m}$, $a = 0.0125$ m, $y = 0.5$ m.

(a) Hemisphere

$$r = \frac{\rho}{2\pi R} = \frac{100}{2\pi \times 20} = 0.796\ \text{m}$$

(b) Driven rod

$$20 = \frac{100}{2\pi L}\ln\frac{2L}{0.0125}$$

This is solved by trial:

$$L \approx 5.38\ \text{m} \quad \left(\ln\frac{2 \times 5.38}{0.0125} = 6.757\right)$$

(c) Counterpoise

$$\sqrt{2ay} = \sqrt{2 \times 0.0125 \times 0.5} = 0.1118\ \text{m}$$ $$20 = \frac{100}{\pi L}\left[\ln\frac{2L}{0.1118} - 1\right]$$ $$L \approx 5.80\ \text{m} \quad \left(\ln\frac{2 \times 5.80}{0.1118} = 4.641\right)$$

Answer: hemisphere radius = 0.796 m; driven rod length = 5.38 m; counterpoise length = 5.80 m (at 0.5 m depth).

In practice the rod or counterpoise is preferred, since a 0.8 m radius hemisphere is hard to make; in high-resistivity soil several rods or longer counterpoises are used in parallel.

Earthing (grounding) is the connection of electrical systems and equipment to the general mass of earth through a low-resistance path. It is done for safety of people, protection of equipment and stable system operation.

A. By purpose

1. System (neutral) earthing: the neutral of generators and transformers is connected to earth. It fixes the system voltage with respect to earth and allows earth-fault protection to work.
2. Equipment (body) earthing: non-current-carrying metal parts (motor frames, panels, tower bodies) are earthed so that a fault does not leave a dangerous voltage on them.
3. Lightning/surge earthing: lightning arresters, earth wires and towers are earthed to discharge surge currents.

B. Methods of neutral (system) earthing

C. Earth electrode types (equipment earthing)

1. Plate earthing: a copper (60 × 60 cm, 3 mm) or GI plate buried vertically about 3 m deep, surrounded by charcoal and salt to keep moisture.
2. Pipe earthing: a GI pipe (about 38 mm diameter, 2.5 m long) with holes, driven vertically, with alternate layers of charcoal and salt; water poured through a funnel. Most common for buildings.
3. Rod earthing: copper or copper-bonded steel rods driven into the soil; used in sandy soil.
4. Strip or wire earthing: copper/GI strips buried horizontally at about 0.5 m depth; used in rocky soil.
5. Counterpoise: buried wires along transmission lines to reduce tower footing resistance.
6. Earth mat/grid: mesh of conductors under a substation, giving low resistance and equipotential surface.

   Pipe earthing
   funnel --o
            |  GI pipe with holes
   ground --+------------
            |   charcoal + salt
            |   layers
            |
           ~2.5 m deep

D. LV system earthing (IEC)

TN-S, TN-C, TN-C-S, TT and IT systems, depending on how source and exposed parts are earthed.

Step and touch potentials

When fault current $I_g$ flows into the earth through an electrode or substation grid, the soil around it rises in potential, with a gradient on the surface.

• Step potential: the voltage between the two feet of a person standing on the ground, about 1 m apart, without touching any earthed object.
• Touch potential: the voltage between a person's hand touching an earthed structure and their feet on the ground, at about 1 m horizontal distance.

  GPR  ___  structure
      |   |  hand
      |   |   \o    touch: hand-to-feet
  ____|___|___/|\___ ground
              / \      step: foot-to-foot
       potential falls with distance

Why a person gets an electric shock

A shock occurs when the body becomes part of a closed circuit and a current passes through it. This happens when:

1. A person touches a live conductor and earth at the same time, or two conductors at different potential.
2. Insulation fails and a metal frame becomes live, and the frame is not properly earthed or protection does not trip.
3. During an earth fault, the ground near an electrode rises in potential and a person bridges a step or touch voltage.
4. Induced voltage on de-energised lines near live lines, or stored charge in capacitors and cables.

The current is $I = V/(R_b + R_{contact})$; human body resistance is about $1000\ \Omega$. Above about 10 mA the person cannot let go, and around 50–100 mA ventricular fibrillation can occur.

Safety precautions

1. Proper equipment and system earthing; low-resistance substation earth mat with equipotential bonding.
2. Surface layer of crushed rock (high resistivity) in switchyards to cut step and touch current.
3. Fast protective relays, fuses and RCDs (30 mA) to cut the fault quickly.
4. Isolate, lock-out, tag-out, test for dead and earth the circuit before work.
5. Use insulated tools, rubber gloves, boots, mats and helmets of proper rating.
6. Keep safe clearance; use fences, barriers and danger signs.
7. Only trained and authorised persons, with work permits for HV work.
8. Regular inspection of insulation and earthing; avoid wet conditions.

Safety regulations

• Safe step and touch voltage limits as per IEEE Std 80:

$$E_{step} = (1000 + 6C_s\rho_s)\frac{0.116}{\sqrt{t_s}},\qquad E_{touch} = (1000 + 1.5C_s\rho_s)\frac{0.116}{\sqrt{t_s}}$$

• Wiring and earthing codes (IEC 60364, IS 3043, National Electrical Code).
• In Nepal: the Electricity Act 2049 and Electricity Regulations 2050 set rules for safety, clearances and licensing, and NEA follows its own safety manual and earthing standards.

An electric shock is the effect produced when current flows through the human body. The body reacts to the current, so its effects depend on the magnitude of current, the path, the duration and the frequency.

Physiological effects of electric shock

1. Sensation and pain: small currents stimulate nerves and cause tingling and pain.
2. Muscular contraction (tetanus): current stimulates muscles; the hand grips the conductor and cannot let go, increasing the duration of shock.
3. Respiratory paralysis: current through the chest affects breathing muscles and the brain's breathing centre, causing suffocation.
4. Ventricular fibrillation: current through the heart disturbs its rhythm; the ventricles quiver instead of pumping, and blood circulation stops. This is the main cause of death.
5. Cardiac arrest: large currents stop the heart completely (it may restart after the current is removed).
6. Burns: heating ($I^2Rt$) at the contact points and inside tissue; arc burns from high-voltage flashes.
7. Nerve and brain damage, loss of consciousness, and later kidney failure due to muscle breakdown.
8. Secondary injuries: falls from height and injuries from involuntary movement.

Effects of electric current in the human body (50/60 Hz, about 1 s, hand to feet)

Dalziel's safe body current relation for fibrillation threshold:

$$I_b = \frac{k}{\sqrt{t}}, \quad k = 0.116 \text{ (50 kg)},\ 0.157 \text{ (70 kg)}$$

For example, for $t = 0.5$ s and a 50 kg person, $I_b = 0.116/\sqrt{0.5} = 0.164$ A.

Factors deciding the severity

• Magnitude of current = voltage ÷ body resistance (dry skin up to 100 kΩ, wet skin about 1 kΩ).
• Path: hand to hand or hand to foot (through the heart) is most dangerous.
• Duration: longer time lowers the safe current.
• Frequency: 50–60 Hz is the most dangerous; DC and high frequency are less likely to cause fibrillation.
• Body condition: weight, health, heart condition, moisture and contact area.

Why improper earthing leads to high electric potential

When an earth fault occurs, the fault current $I_f$ flows through the earth electrode of resistance $R_g$. The electrode and all connected metal parts rise to the ground potential rise (GPR):

$$V = I_f R_g$$

• If the earthing is poor (high $R_g$ due to dry soil, corroded or loose connections, too few electrodes), $V$ becomes large. For example, $I_f = 1000$ A with $R_g = 10\ \Omega$ gives $V = 10$ kV on the equipment frame, while with $R_g = 1\ \Omega$ it is only 1 kV.
• High $R_g$ also limits the fault current, so fuses or relays may not trip, and the frame stays live for a long time.
• If the frame is not earthed at all, a body touching it becomes the only path to earth and gets the full phase voltage.
• Poor earth-mat design gives steep surface voltage gradients, so step and touch potentials exceed safe values.
• In ungrounded systems an earth fault raises healthy-phase voltage to line value, and arcing grounds can produce 5–6 pu overvoltages.
• Lightning current through a high tower footing resistance causes high tower-top voltage and back-flashover.

So improper earthing creates dangerous potentials on equipment and ground, threatens people and damages insulation.

System grounding in common practice

1. Generators: neutral earthed through a high resistance or a distribution transformer with a secondary resistor, to limit stator earth-fault current to a few amperes.
2. Transmission (66 kV and above): solid (effective) earthing of transformer neutrals, so that healthy-phase voltage stays below 80% of line voltage ($X_0/X_1 \le 3$, $R_0/X_1 \le 1$). This allows reduced insulation and surge arrester ratings. NEA's 132/220/400 kV systems are effectively earthed.
3. Distribution (11/33 kV): solid earthing, or resistance/reactance earthing to limit fault current; resonant (Petersen coil) earthing is used in some countries for overhead networks.
4. LV (400/230 V): neutral solidly earthed at the transformer (TN or TT systems); consumer installations have equipment earthing and RCDs.
5. Delta systems: a zig-zag earthing transformer provides an artificial neutral.
6. Substations: an earth mat (grid) of copper or GI conductors buried 0.5–1 m deep, with earth rods, bonding all equipment frames, fences and structures, covered with crushed gravel; designed per IEEE 80 so that step and touch voltages are safe.
7. Transmission lines: overhead earth wires bonded to each tower; tower footing resistance kept low (below about 10–20 Ω) with rods or counterpoises.

When fault current flows into the earth through an electrode, tower or substation grid, the soil near it rises in potential. The potential is highest at the electrode and falls with distance, so the ground surface has a voltage gradient. A person in this area can bridge part of this voltage.

Step potential

Step potential is the voltage difference between two points on the ground surface one step (about 1 m) apart, experienced between the feet of a person walking near the electrode. Current flows foot to foot (through legs), so it is less dangerous than touch, but a fall can turn it into a worse contact.

Touch potential

Touch potential is the voltage between an earthed metal structure that a person touches with the hand and the ground surface where the person stands (about 1 m away). Current flows hand to feet, through the heart, so it is more dangerous. The mesh potential (largest touch voltage in a grid mesh) and transferred potential are special cases.

 V (potential)
 |\
 | \   GPR at electrode
 |  \___
 |      \____
 |  Et       \______ Es
 +--|---|-----|-|------> distance
    hand feet  foot foot
   (touch)     (step, 1 m)
       structure at GPR

Equivalent circuits

 Touch:  structure--Rb--[feet in parallel: Rf/2]--earth
 Step:   foot--Rf--Rb--Rf--foot (feet in series)

With foot resistance $R_f \approx 3\rho_s$ and body resistance $R_b = 1000\ \Omega$, the tolerable limits (IEEE 80, 50 kg person) are:

$$E_{touch} = (R_b + 1.5\rho_s)\frac{0.116}{\sqrt{t_s}}, \qquad E_{step} = (R_b + 6\rho_s)\frac{0.116}{\sqrt{t_s}}$$

A surface layer of crushed rock (high $\rho_s$) and a closely spaced earth grid keep these potentials safe.

Effects of electric shock

Current through the body causes tingling and pain (about 1 mA), muscular contraction and inability to let go (about 10–20 mA), breathing difficulty (about 25–60 mA), ventricular fibrillation (about 60–100 mA and above), cardiac arrest and burns at higher currents, plus nerve damage and secondary injuries from falls.

Why and how DC and AC of different frequencies differ

The body's nerves and heart work on electrical signals of low frequency. The effect depends on how strongly the current repeatedly stimulates nerves and heart muscle.

1. DC: a steady current stimulates nerves mainly when it is switched on or off, so muscles do not stay in continuous spasm. The let-go and fibrillation thresholds are about 2–4 times higher than for 50 Hz AC (let-go roughly 50–90 mA). DC can still cause burns and electrolysis of body fluids.
2. AC at 50–60 Hz: this is the most dangerous range. Each cycle restimulates the muscles, causing continuous tetanic contraction, so the victim grips the conductor and cannot let go, and the heart is easily thrown into fibrillation.
3. Higher frequency (above about 1 kHz): nerves cannot respond to each cycle, and current tends to flow near the surface of the body (skin effect). Thresholds of perception, let-go and fibrillation rise with frequency. At very high frequency (above about 100 kHz) the main danger is heating and burns rather than fibrillation.

Earth resistivity $\rho$ is measured to design earthing systems (substation grids, tower footings). The common methods use an earth tester that injects current $I$ and measures voltage $V$, giving $R = V/I$.

1. Wenner four-electrode method

Four electrodes are placed in a straight line at equal spacing $a$, driven to a depth $b \ll a$. Current is passed between the outer pair (C1, C2); voltage is measured between the inner pair (P1, P2).

   C1      P1      P2      C2
 --|-------|-------|-------|--
   |<- a ->|<- a ->|<- a ->|

Potential due to a point source at the surface is $\frac{\rho I}{2\pi r}$. By superposition:

$$V = \frac{\rho I}{2\pi}\left[\left(\frac{1}{a}-\frac{1}{2a}\right) - \left(\frac{1}{2a}-\frac{1}{a}\right)\right] = \frac{\rho I}{2\pi a}$$ $$\rho = 2\pi a R$$

Readings at increasing spacing give resistivity at increasing depth (about depth $a$).

2. Schlumberger (Schlumberger–Palmer) method

The potential electrodes are kept close together (spacing $d$), and the current electrodes are placed at distance $c$ outside each potential electrode. Only the current electrodes are moved for deeper readings, so it is faster and more sensitive for large spacings.

   C1          P1  P2          C2
 --|-----------|---|-----------|--
   |<--- c --->|<d>|<--- c --->|

$$\rho = \frac{\pi c(c+d)R}{d}$$

For $c = d = a$ this gives $\rho = 2\pi aR$, the Wenner case.

3. Driven-rod (three-point / variation-of-depth) method

A test rod of length $L$ and diameter $d$ is driven into the soil, and its resistance $R$ is measured by the fall-of-potential method using a current probe C (far away, at least 5–10 times rod length) and a potential probe P at about 62% of that distance.

  Earth tester
   E      P            C
 --|------|------------|--
   |<-0.62D->|
   |<-------- D ------->|
   test rod

$$\rho = \frac{2\pi L R}{\ln\left(\dfrac{8L}{d}\right) - 1}$$

Repeating with the rod driven deeper gives the change of resistivity with depth. It is simple and suited to small areas but measures only the soil near the rod.

Practical points

• Take readings in several directions and at several spacings; use the dry-season (highest) value for design.
• Use AC or reversing DC to avoid polarisation and errors from stray currents.
• Keep test leads away from buried metal pipes and cables, which distort the readings.

Earthing techniques commonly practised in industry

1. Pipe earthing: perforated GI pipe (about 38 mm, 2–3 m long) in a pit with charcoal and salt; most common for buildings and small installations.
2. Plate earthing: copper or GI plate (600 × 600 mm) buried about 3 m deep with charcoal and salt.
3. Rod earthing: copper-bonded steel rods driven into the ground; easy where soil is soft.
4. Strip/wire earthing: horizontal copper or GI strips buried 0.5 m deep; used in rocky soil.
5. Chemical (maintenance-free) earthing: electrode with conductive backfill compound such as bentonite.
6. Earth mat/grid: horizontal mesh with vertical rods for substations and power plants.
7. Counterpoise and tower footing: buried wires/rods for transmission towers.
8. Neutral earthing of the system: solid, resistance, reactance or resonant earthing of transformer and generator neutrals.
9. Equipment earthing and bonding: frames, enclosures, cable sheaths and structures bonded to the earth bus; double earthing of major equipment.
10. Lightning protection earthing: separate earth pits for arresters and lightning conductors, bonded to the main grid.

How a properly designed substation earthing protects people

During an earth fault, fault current $I_g$ flows into the soil and the whole grid rises to $GPR = I_g R_g$. The danger to a person is not the GPR itself but the difference in potential across the body (step, touch, mesh and transferred potentials). A good design (IEEE Std 80) keeps these differences below safe limits:

   ____  ____  ____  earth mat (mesh)
  |    ||    ||    |  0.5-1 m deep
  |____||____||____|  + vertical rods
  |    ||    ||    |
  |____||____||____|
   gravel layer on top, fence bonded

1. Low grid resistance: a large grid with many rods lowers $R_g$ and thus the GPR.
2. Equipotential area: the closely spaced mesh makes the ground surface nearly the same potential as the equipment, so touch and mesh voltages are small. Finer mesh is used near equipment operated by people.
3. Bonding of all metal: frames, structures, fences, cable sheaths and gates are bonded to the grid, so a person touching them stands on ground at nearly the same potential.
4. High-resistivity surface layer: 10–15 cm of crushed rock (2000–3000 Ω-m) greatly increases foot contact resistance and reduces body current.
5. Grading rings and perimeter conductors outside the fence reduce steep gradients at the edge and step voltage outside.
6. Fast fault clearing: low $R_g$ gives enough fault current for relays to trip quickly; shorter $t_s$ allows larger safe voltages:

$$E_{touch} = (1000 + 1.5C_s\rho_s)\frac{0.116}{\sqrt{t_s}}$$

7. Control of transferred potential: isolation of communication circuits and care with fences and rails leaving the yard.
8. Low earth-conductor impedance so that lightning and switching surges are discharged safely.

Thus a well-designed earth mat makes the substation an equipotential zone where actual step and touch voltages remain below the tolerable values, so personnel do not receive a dangerous shock.

Electrical safety rules are practices and legal requirements that protect people and equipment from shock, burns, fire and explosion.

Basic safety rules

1. Work on a circuit only after it is switched off, isolated, locked and tagged (lock-out/tag-out).
2. Test for dead with a proper tester and earth/short the conductors before touching them; treat every circuit as live until proven dead.
3. Use insulated tools, rubber gloves, boots, mats, helmets and face shields of correct voltage rating.
4. Keep safe clearance from live parts; use barriers, fences and danger boards.
5. All metal frames must be properly earthed; use RCD/ELCB on socket circuits.
6. Use correctly rated fuses, MCBs and cables; never bypass protection.
7. Do not work on electrical equipment with wet hands or in wet conditions.
8. Only trained and authorised persons should operate or repair HV equipment; use work permits for HV work.
9. Discharge capacitors and cables before handling.
10. Keep fire extinguishers (CO2, dry powder) nearby; never use water on live equipment.
11. Learn first aid and CPR; display shock-treatment charts.

Regulations

• Nepal: the Electricity Act 2049 (1992) and Electricity Regulations 2050 (1993) cover licensing, safety, clearances of lines from buildings and ground, and responsibility for accidents; NEA safety rules and the Nepal Electricity Authority Act apply to utility work.
• International/standards: IEC 60364 (LV installations), IEEE Std 80 (substation earthing), IS 3043 (earthing), IEC 61936 (HV installations), and occupational safety codes (e.g. NFPA 70E).
• Regular inspection and testing of insulation resistance, earth resistance and protective devices is required by these codes.

Earth resistivity $\rho$ (Ω-m) is the resistance of a 1 m cube of soil. It must be measured because every earthing design depends on it, and it changes widely (from about 10 Ω-m in wet clay to over 1000 Ω-m in rock) with soil type, moisture, salts and temperature.

Reasons for measuring earth resistivity

1. Design of earth electrodes and substation grids: the earth resistance is directly proportional to $\rho$ (e.g. rod $R = \frac{\rho}{2\pi L}\ln\frac{2L}{a}$). Without $\rho$ the number, size and depth of electrodes cannot be chosen.
2. Safety of personnel: step and touch potentials depend on $\rho$ of the soil and surface layer; IEEE 80 design needs $\rho$ to check safe limits.
3. Tower footing resistance: lightning performance and back-flashover rate of lines depend on footing resistance, which depends on $\rho$.
4. Choice of site and best location for earth pits, and the best depth (layered soil), since resistivity changes with depth.
5. Protection operation: a low earth resistance gives enough fault current for relays to operate quickly.
6. Corrosion assessment: low-resistivity soil is more corrosive for buried metal and pipelines; also needed for cathodic protection design.
7. Geophysical surveys: locating water, ore bodies and rock layers.

It is measured mainly by the Wenner four-electrode method ($\rho = 2\pi aR$), preferably in the dry season to get the worst-case value.

The three common electrodes are a hemisphere, a driven rod and a counterpoise. Using the standard relations (Begamudre, EHV AC Transmission Engineering):

$$\begin{aligned} \text{Hemisphere:}\quad & R = \frac{\rho}{2\pi r} \\ \text{Driven rod:}\quad & R = \frac{\rho}{2\pi L}\ln\frac{2L}{a} \\ \text{Counterpoise:}\quad & R = \frac{\rho}{\pi L}\left[\ln\frac{2L}{\sqrt{2ay}} - 1\right] \end{aligned}$$

Given: $R = 16\ \Omega$, $\rho = 100\ \Omega\text{-m}$, $a = 0.0125$ m, $y = 0.6$ m.

(a) Hemisphere

$$r = \frac{\rho}{2\pi R} = \frac{100}{2\pi \times 16} = 0.995\ \text{m}$$

(b) Driven rod

$$16 = \frac{100}{2\pi L}\ln\frac{2L}{0.0125}$$ $$L \approx 6.98\ \text{m} \quad \left(\ln\frac{2 \times 6.98}{0.0125} = 7.018\right)$$

(c) Counterpoise

$$\sqrt{2ay} = \sqrt{2 \times 0.0125 \times 0.6} = 0.1225\ \text{m}$$ $$16 = \frac{100}{\pi L}\left[\ln\frac{2L}{0.1225} - 1\right]$$ $$L \approx 7.60\ \text{m} \quad \left(\ln\frac{2 \times 7.60}{0.1225} = 4.821\right)$$

Answer: hemisphere radius = 0.995 m; driven rod length = 6.98 m; counterpoise length = 7.60 m (buried 0.6 m deep).

Electric shock is the body's reaction to current passing through it. The current disturbs the electrical signals of nerves, muscles and heart and heats the tissues.

Physiological effects

Main effects explained:

1. Nerve stimulation and pain.
2. Tetanic muscle contraction: the hand grips the conductor, so the shock lasts longer.
3. Respiratory arrest: chest muscles and the brain's breathing centre are paralysed.
4. Ventricular fibrillation: the heart quivers and stops pumping blood; death follows in minutes without defibrillation.
5. Burns: contact burns, arc burns and internal burns from $I^2Rt$ heating.
6. Other: unconsciousness, nerve and brain damage, kidney damage, falls and fractures.

Factors affecting the magnitude of damage

1. Magnitude of current: the most important factor; $I = V/R_{body}$.
2. Duration of current: the safe current falls with time. Dalziel's relation for fibrillation threshold:

$$I_b = \frac{0.116}{\sqrt{t}}\ \text{A (50 kg)}, \qquad I_b = \frac{0.157}{\sqrt{t}}\ \text{A (70 kg)}$$

e.g. for 1 s, 116 mA; for 0.1 s, 367 mA (50 kg). 3. Path of current: paths through the heart (hand–hand, left hand–feet) are most dangerous; foot–foot is less dangerous. 4. Body resistance: dry skin can be 100 kΩ, wet or broken skin about 1 kΩ (500 Ω internal). Moisture, sweat, contact area and pressure lower it. 5. Voltage: higher voltage breaks down skin resistance and drives more current; above about 500 V burns become severe. 6. Frequency: 50–60 Hz is most dangerous; DC and high frequencies need larger currents for the same effect. 7. Phase of heart cycle: shock during the T-wave (vulnerable period) easily causes fibrillation. 8. Body weight, age, sex and health: lighter persons, women, children and heart patients have lower thresholds. 9. Contact condition: footwear, floor material and surface layer resistivity (crushed rock) add series resistance. 10. Speed of rescue and first aid: early CPR and defibrillation greatly reduce fatality.

When an earth fault occurs, fault current $I_g$ enters the soil through the earth electrode or substation grid. The grid rises to the ground potential rise

$$GPR = I_g R_g$$

and the ground surface potential falls with distance from the electrode. A person bridging part of this potential gets a shock. Improper earthing (high $R_g$, too few electrodes, wide mesh, no bonding, no surface layer, slow protection) makes these potentials exceed the safe values.

 V
 |\_ GPR = Ig Rg
 |  \       steep gradient
 |   \__    (poor earthing)
 |      \___
 |  Et      \____ Es
 +---|--|-----|-|------> distance
   structure  feet 1 m apart

Touch potential

Voltage between the hand on an earthed structure and the feet standing 1 m away. Equivalent circuit: body resistance $R_b$ in series with two feet in parallel ($R_f/2$), where $R_f \approx 3\rho_s$:

$$I_b = \frac{E_{touch}}{R_b + 1.5\rho_s}$$

Step potential

Voltage between two feet 1 m apart. Body $R_b$ in series with two feet ($2R_f$):

$$I_b = \frac{E_{step}}{R_b + 6\rho_s}$$

Safe (tolerable) limits (IEEE 80, 50 kg person)

Using Dalziel's current $I_b = \frac{0.116}{\sqrt{t_s}}$ and $R_b = 1000\ \Omega$:

$$E_{touch,50} = (1000 + 1.5C_s\rho_s)\frac{0.116}{\sqrt{t_s}}, \qquad E_{step,50} = (1000 + 6C_s\rho_s)\frac{0.116}{\sqrt{t_s}}$$

$C_s$ is the surface-layer derating factor and $t_s$ the fault duration.

How improper earthing makes them unsafe

1. High grid resistance $R_g$: GPR $= I_gR_g$ is large, so actual touch voltage (a fraction of GPR) is large. For example, $I_g = 2$ kA and $R_g = 5\ \Omega$ gives GPR = 10 kV; even 30% of this (3 kV) as touch voltage is far above the safe value of a few hundred volts.
2. Wide mesh or no grid: surface potential is not uniform; mesh (touch) voltage

$$E_m = \frac{\rho K_m K_i I_g}{L_M}$$

rises when the total buried length $L_M$ is small. 3. Steep gradient at the edge (no grading ring): high step voltage

$$E_s = \frac{\rho K_s K_i I_g}{L_S}$$

4. No surface layer of crushed rock: low $\rho_s$, so tolerable voltages drop.
5. Unbonded equipment or fences: the full GPR may appear as touch voltage.
6. High $R_g$ reduces fault current so relays may be slow; longer $t_s$ lowers the tolerable limits.

Remedies

Lower $R_g$ (more rods, larger grid, deep electrodes, chemical backfill), closer mesh spacing, bonding of all metal parts, a crushed-rock surface layer, grading rings, and fast fault clearing so that $E_{actual} < E_{tolerable}$.