Meter Bridge for Unknown Resistance Explained for School

A meter bridge is a clever sliding-contact version of the Wheatstone bridge. It uses a one-metre-long uniform wire and a balance condition to find an unknown resistance accurately. Instead of knowing all four resistors, you only need one known resistance and two lengths measured along the wire.

It is needed because unknown resistors in circuits, faulty wires and material samples often cannot be trusted from colour codes alone. The meter bridge gives a null method, so the galvanometer draws almost no current at balance and the result is not affected by its resistance.

Key Concepts

Principle: Wheatstone bridge balance, P/Q = R/S, where P and Q are resistances of wire segments and S is the standard known resistance. Uniform wire: resistance is proportional to length, R = ρl/A. Jockey: sliding contact that searches for the null point. Null point: position where galvanometer shows zero deflection. End correction: small error due to non-zero resistance at the wire ends and contacts.

Formulas

X = S × l/(100 − l) where X is unknown resistance in ohm (Ω), S is standard resistance in Ω and l is length from the left end to the null point in centimetre (cm), total wire length 100 cm. Balance condition: R_wire_left / R_wire_right = X / S. Assumption: wire is uniform in cross-section and made of a material with constant resistivity at constant temperature. Limit: accuracy falls if the null point is very close to either end, because a small length error becomes a large percentage error.

Worked Example

Standard S = 10 Ω. The null point is found at l = 40 cm from the left where the unknown X is connected.

1. Right segment length = 100 − 40 = 60 cm.
2. Apply X = S × l/(100 − l) = 10 × 40/60.
3. X = 400/60 = 6.67 Ω.

So the unknown resistor is about 6.7 Ω. Repeating with a different S that brings l near 50 cm would reduce percentage error further.

Common Misconceptions

• Any null point is equally good: False. A point near 0 or 100 cm magnifies errors, so choose S so balance lies near the middle.
• The galvanometer resistance affects balance: At exact null it carries no current, so it does not affect the ratio.
• Parallax errors do not matter: Reading the jockey position from an angle shifts l and directly shifts the calculated X.

Real-World Applications

• School and college laboratories for measuring unknown resistors and resistivity of wires.
• Finding fault location in cables by adapting the bridge to a Murray loop test.
• Calibration of low-value resistors and checking heating elements.

In short, the meter bridge turns a resistance comparison into a length comparison on a uniform wire, making unknown resistance easy to find with just a standard box and a galvanometer.