---
title: "Potential difference, emf, resistivity"
subject: "Basic Electrical Engineering"
chapter: 1
key: "semester_1/basic_electrical_engineering:emf-pd-resistance-resistivity"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/emf-pd-resistance-resistivity
site: BCT Engineering
---

# Potential difference, emf, resistivity

Basic Electrical Engineering · Chapter 1: General Electric System

- Asked in: 2068 Shrawan, 6 marks
- Video: [Potential Difference vs. Electromotive Force - A Level Physics](https://www.youtube.com/watch?v=v7XQs2sKsKU) — Physics Online
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/emf-pd-resistance-resistivity
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-1

## Question

What is the difference between the potential difference and electromotive force? Define resistance and resistivity.

## Short answer

EMF is the energy supplied per unit charge by a source; potential diference is the energy used per unit charge between two points. EMF exists in source, PD across any element. Resistnce R=V/I (Ω) opposes current; resitivity ρ is a material's intrinsik property (Ω·m), R=ρl/A.

## Answer

#### Difference between potential difference and EMF

| Point | EMF | Potential difference |
|---|---|---|
| Meaning | Energy supplied by the source per unit charge | Energy used between two points per unit charge |
| Exists in | Source only | Any two points / element |
| With no current | Present | Zero across a resistor |
| Value | Larger (E = V + I r) | Smaller than EMF for a loaded source |
| Cause | Chemical or magnetic action | Current through a resistance |

#### Resistance
**Resistance** is the opposition offered by a material to the flow of current: R = V/I (ohm, Ω). For a conductor, R = ρ l/A, so it depends on length, area, material and temperature.

#### Resistivity
**Resistivity (ρ)** is the resistance of a unit cube of the material, measured between opposite faces: ρ = R A/l, in Ω·m. It depends only on the material and its temperature, not on its dimensions. Its reciprocal is conductivity σ = 1/ρ (S/m).

Example: copper has ρ ≈ 1.7 × 10⁻⁸ Ω·m; nichrome ≈ 1.1 × 10⁻⁶ Ω·m, so nichrome is used for heating elements.

## Check yourself

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

1. With no current flowing, which is true?
   A. EMF is zero and the PD across a resistor is E
   B. EMF is present and the PD across a resistor is zero
   C. Both are zero
   D. Both are equal to I r
   Answer: B. EMF is a source property that exists regardless of current; PD across a resistor needs current. (Key point: EMF vs PD with no current)

2. For a loaded source, EMF compared with terminal PD is:
   A. Smaller, since E = V - I r
   B. Equal always
   C. Larger, since E = V + I r
   D. Unrelated
   Answer: C. Some EMF is lost across the internal resistance, so E = V + I r. (Key point: Relation)

3. Resistivity rho = R A / l depends on:
   A. Material and temperature, not on dimensions
   B. Length only
   C. Area only
   D. Current through it
   Answer: A. Resistivity is a material property, independent of the shape of the conductor. (Key point: Resistivity)

4. Conductivity sigma is related to resistivity by:
   A. sigma = rho
   B. sigma = rho^2
   C. sigma = 1 - rho
   D. sigma = 1/rho, in S/m
   Answer: D. Conductivity is the reciprocal of resistivity. (Key point: Conductivity)

## Related in Basic Electrical Engineering

- [Potential difference versus emf](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Apotential-difference-vs-emf) — Basic Electrical Engineering, chapter 1
- [Explain emf, potential difference and current](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aemf-potential-difference-current) — Basic Electrical Engineering, chapter 1
- [Resistance, resistivity and factors](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aresistance-resistivity-factors) — Basic Electrical Engineering, chapter 1

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