Wheatstone Bridge, Ammeters & Voltmeters
Measuring resistance by a null, and meters that disturb little.
Lesson at a glanceShow the key points
- Balanced bridge: no galvanometer current, R₁/R₂ = R₃/R₄ (32.15).
- Ammeter: coil with a small parallel shunt, in series; resistance R_cr/(R_c + r) must be small.
- Voltmeter: coil with a large series resistance, in parallel; resistance must be large.
- Galvanometer: centre-zero meter for current in either direction.
Measuring electricity means putting an instrument into the circuit. The Wheatstone bridge measures resistance by finding a null; ammeters and voltmeters are designed to disturb the circuit as little as possible.
The Wheatstone bridge
Four resistors R₁, R₂, R₃, R₄ form a loop with corners A, C, B, D. A cell is joined across A and B, and a galvanometer (a sensitive meter whose needle swings left or right with the current direction) across C and D.
For one particular set of values no current flows through the galvanometer: the bridge is balanced. Then VC = VD, R₁ and R₂ carry the same current, and so do R₃ and R₄. Comparing the drops, (VA − VC)/(VC − VB) = R₁/R₂ and (VA − VD)/(VD − VB) = R₃/R₄. With VC = VD these ratios are equal:
To measure an unknown R₄, make R₃ variable and adjust it until the galvanometer reads zero; then R₄ = R₂R₃/R₁.
In a bridge, the arms from A are 15 Ω (to C) and R (to D); the arms to B are 30 Ω (from C) and 50 Ω (from D). A 100 Ω resistor joins C and D. For what R is there no current in the 100 Ω?
Ammeters and voltmeters
Both contain a coil hung between magnet poles; current through the coil turns it, and a needle fixed to it moves along a scale by an amount proportional to the current.
Ammeter
It goes in series with the part whose current you want, current entering at the + terminal. A small resistance r, the shunt, is joined in parallel with the coil (resistance Rc), so the coil takes only a fixed fraction of the current, i₁ = ri/(Rc + r). Its total resistance is
A galvanometer is built the same way but with its zero in the middle of the scale, so it shows current in either direction.
An ammeter made of a 90 Ω coil with a 10 Ω shunt is in series with a 51 Ω resistor across a 6.0 V ideal cell. What does it read, and how much current goes through its coil?
Voltmeter
It goes in parallel with the part whose voltage you want, + terminal to the higher potential. A large resistance R is joined in series with the coil, so the coil current is V/(Rc + R), proportional to V. Its resistance Rc + R must be large, so that it draws little current and barely changes the voltage it measures.
A coil of 50 Ω gives full-scale deflection at 1.0 mA. What series resistance turns it into a 0–10 V voltmeter?
- 1Wheatstone bridge balanced: R₁/R₂ = R₃/R₄ (32.15), no galvanometer current.
- 2Ammeter: coil + small parallel shunt, connected in series; low resistance.
- 3Voltmeter: coil + large series resistance, connected in parallel; high resistance.
Check yourself
Keep exploring
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