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A galvanometer coil has resistance of 45 Ω, it shows full scale deflection for a current of 2 mA. What is the required series resistance to convert the galvanometer into a voltmeter of range 0 to 3 V?

Asked in GSEB Board July 2023 · Conversion to ammeter and voltmeter

• (1) 1455 Ω
• (2) 4500 Ω
• (3) 1545 Ω
• (4) 1500 Ω

Step-by-step solution

Why the other options are wrong

• (2) No single slip produces 4500 Ω. Sanity check: R=V/(I_g)-G=3/(2×10⁻³)-45=1500-45=1455 Ω.
• (3) 1545 Ω adds the galvanometer's own 45 Ω instead of subtracting it. The series resistance only has to make up the gap between the 1500 Ω the range needs and the 45 Ω already present.
• (4) 1500 Ω is V/(I_g), the total resistance the branch must have at full scale. The coil already provides 45 Ω of it, so only 1455 Ω is added in series.

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