---
title: "Arrester current and resistance (Z = 300 Ω)"
subject: "High Voltage Engineering"
chapter: 4
key: "semester_8/high_voltage_engineering:arrester-750kv-z300"
source: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/arrester-750kv-z300
site: BCT Engineering
---

# Arrester current and resistance (Z = 300 Ω)

High Voltage Engineering · Chapter 4: Insulation Coordination

- Asked in: 2070 Bhadra, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/arrester-750kv-z300
- Whole chapter: https://www.bctengineer.com/md/semester_8/high_voltage_engineering/chapter-4

## Question

For a 750 kV line, take Vw = 3000 kV crest, travelling on the line and Vp = 1700 kV. The line surge impedance is Z = 300 ohms. Calculate (a) the current flowing in the line before reaching the arrestor, (b) the current through the arrestor, and (c) the value of arrestor resistance for this condition and also find the reflection and refraction coefficient of voltage.

## Short answer

Line current before arrester is 10 kA. Arrester current is 14.33 kA, arrester resistance 118.6 Ω. Voltage reflection coefficient is -0.433 and refraction coefficient 0.567.

## Answer

When the surge reaches the arrester, the arrester conducts and holds the voltage at its protective level $V_p$. It acts as a shunt resistance $R_a$ at the end of the line, and the travelling-wave relations give the currents.

#### Data
- Incident surge, $V_w = 3000$ kV (crest)
- Protective level, $V_p = 1700$ kV
- Line surge impedance, $Z = 300\ \Omega$

#### (a) Current in the line before reaching the arrester
$$
I_w = \frac{V_w}{Z} = \frac{3000}{300} = 10\ \text{kA}
$$

#### (b) Current through the arrester
Reflected voltage: $V_r = V_p - V_w = 1700 - 3000 = -1300$ kV. Reflected current: $I_r = -V_r/Z = 4.33$ kA.
$$
\begin{aligned}
I_a &= I_w + I_r = \frac{2V_w - V_p}{Z} \\
&= \frac{6000 - 1700}{300} = 14.33\ \text{kA}
\end{aligned}
$$

#### (c) Arrester resistance
$$
R_a = \frac{V_p}{I_a} = \frac{1700}{14.333} = 118.6\ \Omega
$$

#### Reflection and refraction coefficients of voltage
$$
\begin{aligned}
\beta &= \frac{R_a - Z}{R_a + Z} = \frac{118.6 - 300}{418.6} = -0.433 \\
\alpha &= \frac{2R_a}{R_a + Z} = \frac{237.2}{418.6} = 0.567
\end{aligned}
$$
Check: $\alpha = 1 + \beta = 0.567$, and $\alpha V_w = 0.567 \times 3000 = 1700$ kV $= V_p$.

| Quantity | Value |
|---|---|
| Line current before arrester | 10 kA |
| Reflected voltage | −1300 kV |
| Arrester current | 14.33 kA |
| Arrester resistance | 118.6 Ω |
| Voltage reflection coefficient | −0.433 |
| Voltage refraction coefficient | 0.567 |

The arrester current (14.33 kA) is larger than the line current (10 kA) because the negative reflected voltage wave carries a positive current. The arrester must be rated for this current.

**Answer: (a) 10 kA, (b) 14.33 kA, (c) $R_a = 118.6\ \Omega$; $\beta = -0.433$, $\alpha = 0.567$.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What current flows in the line before the wave reaches the arrester?
   A. 14.33 kA
   B. 5.67 kA
   C. 1.7 kA
   D. 10 kA
   Answer: D. Iw = Vw / Z = 3000/300 = 10 kA. (Key point: Line current)

2. Why is the arrester current (14.33 kA) larger than the line current?
   A. The negative reflected voltage wave carries a positive current
   B. The arrester generates current
   C. Z doubles at the arrester
   D. The line is lossy
   Answer: A. Vr = -1300 kV gives Ir = +4.33 kA, which adds to the 10 kA incident current. (Key point: Arrester current exceeds line current)

3. What is the arrester resistance?
   A. 300 ohm
   B. 118.6 ohm (Vp / Ia = 1700 / 14.33)
   C. 170 ohm
   D. 237 ohm
   Answer: B. Ra = Vp / Ia = 1700 / 14.333 = 118.6 ohm. (Key point: Arrester resistance)

4. Which relation checks the coefficients?
   A. alpha = beta
   B. alpha = 1 - beta
   C. alpha = 1 + beta, with alpha x Vw = Vp
   D. alpha = 2 beta
   Answer: C. beta = -0.433, alpha = 1 + beta = 0.567, and 0.567 x 3000 = 1700 kV = Vp. (Key point: Voltage coefficients check)

## Close variants set in other exams

- [Arrester current and resistance for 750 kV line](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Aarrester-750kv-z3000) — High Voltage Engineering, chapter 4, asked 2×

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