Metre Bridge: Slide-Wire Bridge

Think of the metre bridge like a see-saw. Just as a see-saw balances when torques on both sides are equal, the bridge "balances" (galvanometer shows zero deflection) when the ratio of resistances on both arms is equal — regardless of how much current flows through the circuit.

A metre bridge (slide-wire bridge) is a practical laboratory device based on the Wheatstone bridge principle, used to measure an unknown electrical resistance by achieving a null-point (balance) condition on a one-metre-long uniform resistance wire.

The metre bridge works on the Wheatstone bridge principle: a bridge circuit is said to be balanced when no current flows through the galvanometer, i.e., points B and D are at the same potential.

Key components:

• A 1-metre-long uniform wire (manganin or constantan) of uniform cross-section
• Two thick copper strips creating three gaps on a wooden board
• A resistance box (R) — known resistance
• An unknown resistance (S) to be measured
• A galvanometer (G) with a sliding jockey
• A battery (Bt) with a key (K) and rheostat

Using the Wheatstone bridge balance condition, with the wire resistance proportional to length:

Equating both:

Solving for S:

• Keep the null point close to the midpoint (30–70 cm) of the wire for higher accuracy
• Avoid prolonged current flow to prevent heating and resistance change
• Use a galvanometer shunt initially to protect it from high currents
• Do not rub the jockey against the wire — this damages the uniform cross-section
• Account for end resistance at the copper strip junctions
• Ensure the wire has uniform cross-section throughout its length

• Not suitable for very low resistances (below ~1 Ω) due to end-resistance errors dominating the measurement
• For low resistances, use Kelvin's Double Bridge or Cary Foster's Bridge instead

Given: R = 6 Ω, balancing length l = 60 cm

Formula: S = R(\[\frac {100−l}{l}\])

Substitution: S = 6 × \[\frac {100−60}{60}\] = 6 × \[\frac {40}{60}\]

Answer: S = 4 Ω

(Battery current in this configuration ≈ 0.66 A, based on total circuit resistance.)