Class 12 Physics Notes: Current Electricity (Chapter 3)
Master Chapter 3 of Class 12 Physics. Understand EMF vs terminal voltage, Kirchhoff's laws, Wheatstone bridge, metre bridge, and resistivity with key formulas and exam PYQs.
Students treat Current Electricity as a formula chapter — memorise V = IR and move on. It is not. The chapter tests conceptual understanding of circuits, and students who rely on formula substitution fail the moment a circuit becomes slightly non-standard.
1. EMF vs. Terminal Voltage
These are not the same quantity. Students who equate them get wrong answers in every problem involving internal resistance.
Formula: Terminal Voltage
V = ε − Ir
- ε = EMF (total energy per unit charge provided by the battery)
- I = current flowing through the circuit
- r = internal resistance of the battery
- V = terminal voltage (actual voltage available at the terminals)
Terminal voltage is always less than EMF when current flows, because some voltage is dropped inside the battery.
2. Kirchhoff's Laws
- KCL (Junction Rule): Sum of currents entering a junction = sum leaving it. Charge cannot accumulate at a node.
- KVL (Loop Rule): Algebraic sum of potential differences around any closed loop = 0.
⚠️ Watch Out! — Sign Convention for KVL
When you traverse a resistor in the direction of current, the potential drops (−IR). When you traverse it against the current, the potential rises (+IR).
When you traverse a battery from − to +, it is a rise (+ε). From + to −, it is a drop (−ε).
Students who do not apply the sign convention consistently arrive at wrong equations and wrong current values.
3. Wheatstone Bridge
The bridge is balanced when no current flows through the galvanometer. The balance condition:
P/Q = R/S
At balance, the potential at both midpoints of the bridge is identical — this is why no current flows through the galvanometer. If the cell and galvanometer are interchanged at balance, the bridge remains balanced. Students who do not understand this symmetry cannot answer this common question.
4. Metre Bridge
A practical implementation of the Wheatstone bridge. The wire of uniform resistance acts as two arms. At balance:
R/S = l/(100 − l)
where l is the balancing length. Students who do not connect the metre bridge to the Wheatstone bridge principle fail modified bridge questions.
5. Resistivity and Resistance — Not the Same
| Quantity | Depends On | Formula |
|---|---|---|
| Resistance (R) | Material, length, cross-section | R = ρL/A |
| Resistivity (ρ) | Material and temperature only | — (material property) |
Stretched wire trap: If a wire is stretched to twice its length, volume is conserved, so A halves. Using R = ρL/A: R becomes ρ(2L)/(A/2) = 4ρL/A = 4R. Resistance becomes 4 times larger, not 2 times.
Summary: Formula Sheet
| Concept | Formula |
|---|---|
| Terminal Voltage | V = ε − Ir |
| Ohm's Law | V = IR |
| Resistance (wire) | R = ρL/A |
| Resistors in Series | R = R₁ + R₂ + R₃ |
| Resistors in Parallel | 1/R = 1/R₁ + 1/R₂ |
| Wheatstone Balance | P/Q = R/S |
| Metre Bridge | R/S = l/(100 − l) |
Practice Questions (PYQs)
- Define EMF of a cell. How is it different from the terminal voltage? Under what conditions are they equal?
- State Kirchhoff's laws. Apply them to find the current in each branch of a circuit with two loops and two batteries.
- A wire of resistance R is stretched to twice its original length. What is its new resistance? Explain using the formula R = ρL/A.
- Why is the Wheatstone bridge method considered more accurate for measuring resistance than Ohm's law method?
- In a metre bridge experiment, the balance point is found at 40 cm from the left end. If the resistance in the right gap is 30 Ω, find the unknown resistance.