Meter BridgeJEE Main

Concept

A meter bridge is a practical Wheatstone bridge built on a 1-metre wire. Slide the jockey until the galvanometer shows zero — at that balance point no current flows through it, and the unknown resistance follows from a simple length ratio.

Key formula

Derivation

The uniform wire's resistance is proportional to length, so the two segments act as the bridge's lower arms with ratio $\ell : (100-\ell)$.

At balance the bridge is null: $\dfrac{R}{X} = \dfrac{\ell}{100-\ell}$. The galvanometer carries no current, so its exact resistance is irrelevant — a key advantage of null methods.

Scenarios to explore

• Meter Bridge — Find an unknown resistance by balancing a wire.
• Balance at 40 cm — A balance point left of centre means the unknown resistor is larger than the known one: X = R(100 − ℓ)/ℓ.

Real-world applications

• Accurate resistance measurement in school & college labs.
• Strain gauges and thermistors read out via bridge circuits.
• Calibrating resistance standards.

JEE exam tips

• Best sensitivity is near the middle (ℓ ≈ 50 cm) — choose $R$ to bring balance there.
• Swapping $R$ and $X$ gaps moves the balance point to $100 - \ell$.

Common mistakes

• Putting the unknown over the known length instead of the matching gap.
• Reading the balance length from the wrong end of the wire.
• Ignoring end-corrections (real wires need them for precision).

Exam traps to avoid

• At balance the galvanometer's resistance does not affect the result.
• A non-uniform wire breaks the length-proportionality and biases the answer.