MIND GROW Magazine

Current Electricity – Stage 1 (IIT–JEE)

Page 10: EMF, Internal Resistance & Maximum Power

1️⃣ EMF of a Cell (ε)

Electromotive Force (EMF) is the energy supplied by a source per unit charge.

ε = Work done per unit charge (J/C)

✔ EMF exists even when no current flows ✔ It is a property of the source, not the circuit

2️⃣ Internal Resistance (r)

Every real cell has resistance inside it called internal resistance.

Cause: Electrolyte + electrodes inside the cell

Internal resistance depends on:

Nature of electrolyte
Distance between electrodes
Temperature
Area of electrodes

3️⃣ Terminal Voltage (V)

Terminal voltage is the potential difference across the external circuit.

V = ε − Ir

I = current in circuit
r = internal resistance

⚠️ When current flows, terminal voltage is less than EMF.

4️⃣ Special Cases

Open circuit (I = 0): V = ε
Short circuit (R = 0): I = ε / r

Short circuit current is maximum and dangerous.

5️⃣ Power Delivered to External Resistance

Power across external resistance R:

P = I²R

Substitute I = ε / (R + r)

P = (ε²R) / (R + r)²

6️⃣ Maximum Power Transfer Theorem

Maximum power is delivered when:
R = r

At this condition:

Current is not maximum
Power is maximum

⚠️ JEE Trap: Students confuse maximum current with maximum power.

7️⃣ Efficiency of a Cell

Efficiency (η):

η = V / ε = R / (R + r)

η → 1 when R >> r
η = 50% when R = r

8️⃣ Graph Insights (JEE Favorite)

V vs I → straight line with slope −r
Intercept on V-axis = ε

Graph questions are guaranteed scoring areas.

9️⃣ Common IIT–JEE Mistakes

Ignoring internal resistance
Wrong terminal voltage formula
Applying R = r blindly

🔑 Final Takeaway – Current Electricity

✔ Ohm’s Law → Simple circuits ✔ Kirchhoff → Complex circuits ✔ EMF & r → Real circuits ✔ Maximum power → Conceptual clarity

🎯 Master these → Current Electricity becomes a guaranteed scoring chapter.

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