Draw the circuit of a Wheatstone bridge and use Kirchhoff's rules to obtain its balance condition. How can the bridge be used to find an unknown resistance?

1. 1 · Define balance. The bridge is balanced when no current flows through the galvanometer, so B and D are at the same potential.
2. 2 · Draw the bridge. [Diamond ABCD: R₂ on AB, R₄ on BC, R₁ on AD, R₃ on DC; G across BD; cell and key across AC; currents marked]
3. 3 · Balance and junctions. At balance I_g = 0, so I₃ = I₁ (junction D) and I₄ = I₂ (junction B).
4. 4 · Loop equations. Loop ADBA: I₁R₁ = I₂R₂. Loop CBDC: I₁R₃ = I₂R₄.
5. 5 · Result. Divide: R₂/R₁ = R₄/R₃.
6. 6 · Finding an unknown. Put the unknown in arm BC (R₄). Keep R₁ and R₂ fixed and vary R₃ until G reads zero. Then R₄ = R₂R₃/R₁. The metre bridge of the practical works on this idea.
7. 7 · Real life. Load sensors in weighbridges and kitchen scales are Wheatstone bridges.
8. 8 · Close in one line. So, a balanced bridge gives an unknown resistance with no current in the galvanometer.

Scoring tip: Label every arm in your diagram the same way as in your equations. A mismatch costs marks.