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A voltmeter has a resistance of G ohm and a range of V volt. The resistance required in series to convert it into a voltmeter of range nV volt is ______.

Asked in GUJCET 2007 · Conversion to ammeter and voltmeter

• (1) nG
• (2) (n-1)G
• (3) G/(n-1)
• (4) G/n

Step-by-step solution

Why the other options are wrong

• (1) nG is the total resistance the new voltmeter must have, not the resistance to be added. The meter's own G is already part of that total, so only nG-G=(n-1)G goes in series.
• (3) G/(n-1) turns the relation upside down. Raising the range means the branch must drop more voltage for the same current, so the added resistance has to be larger than G, and G/(n-1) is smaller than G for every n>2.
• (4) G/n divides where the derivation multiplies. It is smaller than G for n>1, and a small series resistance would barely change the range at all.

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