Shunt and Multiplier Resistances: Extending Meter Ranges

A shunt is a small resistance connected in parallel with a galvanometer to convert it into an ammeter. A multiplier is a large resistance connected in series with a galvanometer to convert it into a voltmeter. Together they are called range-extending resistances because they let one delicate movement measure currents and voltages far beyond its own safe limit.

They matter because a bare galvanometer can carry only a few milliamperes. Without shunts, laboratory ammeters would need a different coil for every range; without multipliers, voltmeters would overload on ordinary batteries. These two simple resistors make practical multirange meters possible.

Key Concepts

Shunt S: low resistance in parallel; most current bypasses the coil. Multiplier R: high resistance in series; most voltage drops across it. Full-scale deflection current Ig: maximum safe current through the coil, in ampere (A). Galvanometer resistance G: coil resistance in ohm (Ω). Range I or V: new full-scale current or voltage after conversion.

Formulas

Shunt for range I: S = Ig G/(I − Ig). Resulting ammeter resistance: RA = G S/(G + S), slightly less than S and always much less than G. Multiplier for range V: R = V/Ig − G. Resulting voltmeter resistance: RV = G + R = V/Ig, in Ω. Assumptions: Ig and G are known constants and the added resistors are non-inductive and temperature stable. Limit: power dissipated in the shunt, I²S, must be within its rating or its value drifts with heating.

Worked Example

G = 50 Ω, Ig = 2 mA = 0.002 A. Find shunt for a 5 A ammeter and multiplier for a 50 V voltmeter.

1. Shunt: S = 0.002 × 50/(5 − 0.002) ≈ 0.10/4.998 ≈ 0.020 Ω.
2. Ammeter resistance ≈ 0.020 Ω, so insertion error stays small.
3. Multiplier: R = 50/0.002 − 50 = 25000 − 50 = 24950 Ω ≈ 24.95 kΩ.

A tiny 0.02 Ω shunt extends current range 2500 times, while a 24.95 kΩ multiplier extends voltage range to 50 V — opposite extremes from the same formula logic.

Common Misconceptions

• A shunt increases meter resistance: Parallel combination always lowers total resistance, which is exactly what an ammeter needs.
• A multiplier is connected in parallel: It is in series; a parallel resistor cannot limit the coil voltage.
• Any wire can serve as a shunt: Shunts need precise low value and low temperature coefficient, usually manganin strips, not ordinary copper.

Real-World Applications

• Multirange ammeters and voltmeters switched in multimeters.
• High-current measurement in battery testing and motor circuits using external shunts.
• High-voltage probes for oscilloscopes and power supplies.

Shunts divert excess current and multipliers drop excess voltage; both protect the same sensitive coil while stretching its range by factors of thousands.