Current Electricity | EMF | Potential Difference

Current Electricity - Potential Difference and EMF of a Cell

current electricity potential difference and emf of a cell is explained with EMF, terminal voltage, open circuit voltage, closed circuit voltage, internal resistance, voltmeter readings, SVG diagrams, graphs and exam-level questions for CBSE, NEET, JEE Main, JEE Advanced, IB, AP, IGCSE and A-Level Physics.

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1. Complete Formula Sheet

EEMF of cell, unit volt.
VTerminal potential difference, unit volt.
I = E/(R+r)Current through complete circuit.
V = E - IrTerminal voltage under load.
E = V + IrEMF equals terminal voltage plus internal drop.
r = (E - V)/IInternal resistance formula.
I = 0 ⇒ V = EOpen circuit condition.
R = 0 ⇒ I = E/rShort circuit current.
R = 0 ⇒ V = 0Terminal voltage in ideal short circuit.
[E]=[V]=ML²T⁻³A⁻¹Dimension of potential difference.
[r]=ML²T⁻³A⁻²Dimension of resistance.
1 V = 1 J C⁻¹Energy per unit charge.

2. What Is EMF?

Electromotive force is the energy supplied by a cell per unit charge. It is not actually a mechanical force; it is a potential difference created by chemical action inside the cell.

Meaning: EMF tells how much energy the cell gives to each coulomb of charge.
Chemical origin: chemical reactions separate charges and maintain potential difference.
Practical example: a 1.5 V cell supplies about 1.5 J of energy per coulomb in open circuit.

3. What Is Potential Difference?

Potential difference is energy consumed or transferred per unit charge between two points. Across a resistor, it represents energy converted into heat. Across cell terminals, it is the actual usable output voltage.

Across resistor: energy per coulomb converted in resistance.
Across cell terminals: terminal voltage available to external circuit.
Role in current: potential difference drives charge flow through a circuit.

4. Open Circuit vs Closed Circuit

Open circuit: I = 0, so V = E - Ir = E. Open circuit potential difference across cell equals EMF.
Closed circuit: I ≠ 0, so V = E - Ir. Terminal voltage is less than EMF.

Proof

1
Terminal voltage is V = E - Ir.
2
Open circuit: I = 0, so V = E.
3
Closed circuit: I is positive, so Ir is positive and V = E - Ir.
4
Therefore, open circuit potential difference is greater than closed circuit potential difference.
Numerical example: If E = 12 V, r = 1 Ω and I = 2 A, then V = 12 - 2 × 1 = 10 V. In open circuit, I = 0 and V = 12 V.

5. Beautiful SVG Diagrams

Cell With E and Internal rEr- terminal+ terminal Open CircuitI = 0V = E Closed CircuitV = E - Ir Cell Connected to RER Voltmeter Across Cell TerminalsVcell terminalsE+- Energy Supplied and LostE per chargeIr lost insideV delivered outside

6. Derivations

Terminal Voltage Equation: V = E - Ir

1
Cell supplies energy per unit charge equal to E.
2
Some energy per unit charge is lost inside the cell as Ir.
3
Usable terminal voltage is V = E - Ir.

EMF Equation: E = V + Ir

1
Start with V = E - Ir.
2
Add Ir to both sides.
3
Therefore E = V + Ir.

Open Circuit Condition

1
Open circuit means no complete path, so I = 0.
2
Put I = 0 in V = E - Ir.
3
Therefore V = E.

Short Circuit Condition

1
Short circuit means external resistance R = 0.
2
Current becomes I = E/(0+r) = E/r.
3
Terminal voltage across external short is V = IR = 0.
4
Power loss inside the cell is I²r = E²/r, which can be dangerous.

7. Important Graphs

V vs IIVEslope = -r V vs Load Resistance RRVV → E as R → ∞ Current vs Load ResistanceRII decreases as R increases

8. Voltmeter Concepts

Open circuit cell: voltmeter draws nearly zero current, so reading = EMF.
Cell delivering current: voltmeter reads terminal potential difference V = E - Ir.
Practical voltmeter: high resistance is used so that current drawn by meter is very small.

9. High Level Conceptual Questions

Why EMF is greater than terminal voltage? Because internal resistance causes a drop Ir inside the cell when current flows.
Why terminal voltage falls under load? More load current means larger Ir drop.
Why EMF remains nearly constant? It depends mainly on cell chemistry and concentration, not directly on load current.
Why old cells show smaller terminal voltage? Their internal resistance increases, so terminal voltage falls more under load.
Why voltmeter measures EMF in open circuit? Current is almost zero, so internal voltage drop is almost zero.
What if internal resistance increases? Current decreases and terminal voltage under load becomes smaller.

10-14. Exam Question Bank With Accordion Solutions

Click any question to open the answer and explanation.

15. Common Student Errors

16. Quick Revision Sheet

EMF: energy supplied per unit charge.
Terminal voltage: usable voltage across terminals.
Open circuit: I = 0, so V = E.
Closed circuit: I ≠ 0, so V = E - Ir.
V-I graph: y-intercept = E and slope = -r.
Voltmeter: reads EMF only when cell is practically open circuit.

Still confused about EMF, Potential Difference, Terminal Voltage, Open Circuit Voltage or Closed Circuit Voltage?

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