1. Kirchhoff's Current Law (KCL) — Junction Rule
Basis: Conservation of charge — charge cannot accumulate at a junction in steady state.
Sign convention: Currents flowing into the junction are positive; currents flowing out are negative.
Example: At a junction where I₁ = 3 A and I₂ = 2 A flow in, and I₃ flows out: I₃ = 3 + 2 = 5 A.
2. Kirchhoff's Voltage Law (KVL) — Loop Rule
Basis: Conservation of energy — net work done around a closed loop = 0 (electrostatic field is conservative).
Sign Convention for KVL
| Element traversed | If traversed along assumed current (or + to −) | If traversed against current (or − to +) |
|---|---|---|
| Resistor R | −IR (voltage drop) | +IR (voltage rise) |
| Battery (EMF ε) | +ε (from − to + inside) | −ε (from + to − inside) |
Steps to Solve Kirchhoff's Problems
- Label all branches with assumed current directions (arrows). If an answer comes negative, actual direction is reversed.
- Apply KCL at each independent junction.
- Apply KVL to enough independent loops (number of loops = number of unknowns − KCL equations).
- Solve the simultaneous equations.
3. Wheatstone Bridge
The Wheatstone Bridge is a circuit with four resistors P, Q, R, S arranged in a diamond (bridge) configuration, with a battery on one diagonal and a galvanometer on the other.
Balanced condition (galvanometer reads zero — no current through it):
When balanced: the bridge can be used to find an unknown resistance — e.g., if P, Q, R are known and S is unknown: S = RQ/P.
Sensitivity: The bridge is most sensitive (galvanometer deflects most for a given change in resistance) when all four resistances are equal.
Example: P = 100 Ω, Q = 200 Ω, R = 150 Ω → S = 150×200/100 = 300 Ω
4. Metre Bridge (Slide Wire Bridge)
The Metre Bridge is a practical implementation of the Wheatstone Bridge using a 1-metre-long uniform resistance wire (manganin or constantan) as two arms of the bridge.
Known resistance R is in one gap; unknown resistance X is in the other. Balance point found at length l from the R side:
Key Points for Metre Bridge
- The wire must be uniform (constant cross-section) so resistance ∝ length.
- Balance point should ideally be near the middle (40–60 cm) for maximum accuracy.
- End corrections are applied in precise experiments (resistance at the metal strips at ends).
- Same principle used in Potentiometer (next topic).
Example: R = 30 Ω, balance at l = 60 cm:
X = 30 × (100−60)/60 = 30 × 40/60 = 20 Ω
