A galvanometer with full-scale deflection of 10 mA is to be converted to a voltmeter with full-scale…

Analyze the question

A galvanometer is converted to a voltmeter by connecting a high resistance (a multiplier) in series with it. At full-scale deflection, the current through the galvanometer is 10 mA and the total voltage across the combination is 5 V.

Concept

Total resistance = V / I_g

Total resistance = R_g + R_series

Solution

1. Convert the current: I_g = 10 mA = 0.010 A
2. Total resistance: R_total = 5 / 0.010 = 500 Ω
3. Subtract the series resistance:

R_g = R_total − R_series = 500 − 498 = 2 Ω

Check: The total resistance is 2 + 498 = 500 Ω, so the current is 5/500 = 0.01 A = 10 mA, which matches the full-scale deflection.

Tip: For voltmeter conversion, use R_series = (V / I_g) − R_g. For ammeter conversion, you use a shunt in parallel instead. Always convert mA to A before calculating.