Academy

Metre Bridge

Practical form of Wheatstone bridge using a uniform wire of length 100 cm. l is the balance length from one end. Unknown resistance S = R(100 − l)/l.
Class 11Class 12
Derivation

Setup

A uniform resistance wire of total length 100 cm is stretched along a scale. Known resistance RR is connected in one gap, unknown SS in the other. A jockey slides along the wire to find the balance point at length ll cm from the RR end.

Applying the Wheatstone balance condition

The wire has uniform resistance per unit length. Resistance of length ll: proportional to ll. Resistance of remaining (100−l)(100 - l): proportional to (100−l)(100 - l).

These act as the PP and QQ arms of the bridge:

P=kl,Q=k(100−l)P = kl, \quad Q = k(100 - l)

At balance: P/Q=R/SP/Q = R/S:

klk(100−l)=RS\frac{kl}{k(100-l)} = \frac{R}{S} RS=l100−l  ⟹  S=R⋅100−ll\boxed{\frac{R}{S} = \frac{l}{100-l} \implies S = R\cdot\frac{100-l}{l}}

Precautions for accuracy

  • Take readings with RR on both sides to eliminate end-corrections
  • Balance point should be near the middle of the wire (avoids sensitivity loss at extremes)
  • Wire must be uniform — non-uniformity introduces systematic error
Note
The metre bridge is a direct application of the Wheatstone bridge principle. Its accuracy is limited by the uniformity of the wire and the sensitivity of the galvanometer.