A student wishes to measure the potential difference across a resistor,R. She has a galvanometer,G and some connecting wires. What else does she need?

Analyze the question She wants to measure potential difference (voltage) using a galvanometer, which only measures very small currents. So she must convert the galvanometer into a voltmeter.

Concept

• A galvanometer converted to a voltmeter needs a high-value resistor in series (called a multiplier).
• A galvanometer converted to an ammeter needs a low-value resistor in parallel (called a shunt).

Why a high resistance in series?

• The galvanometer has a small full-scale current, I_g, and can only handle a small voltage across it.
• The series resistor takes most of the voltage, so the galvanometer current stays within its safe range.
• The total resistance of the meter becomes large: R_total = R_G + R_s. This matters because a voltmeter is connected in parallel across the resistor R. If its resistance is large, it draws very little current and does not disturb the circuit.

The series resistor value is found from:

R_s = (V / I_g) − R_G

where V is the maximum voltage to be measured.

Checking the options

• A. High resistor in parallel with G: this does not limit the current through G, so it is wrong.
• B. Low resistor in parallel with G: this makes an ammeter, so it is wrong.
• C. A resistor in series with G: this is close, but it does not say the resistance is high. A low series resistor would not give a good voltmeter, so it is incomplete.
• D.

Tip Remember: Voltmeter = High resistance in Series, and Ammeter = low resistance in parallel (Shunt). "V-H-S": Voltmeter, High, Series.