A galvanometer of resistance G is converted into a voltmeter of ran...

Question

A galvanometer of resistance G is converted into a voltmeter of range (0 − V) by connecting a resistor of 250 with it. If resistor of 250 is replaced by another resistor of 900 , its range becomes (0 − 3 V). The resistance G of the galvanometer is : v A B

Accepted Answer

Voltmeter conversion: $V=I_g(G+R)$, where $I_g$ is the full-scale galvanometer current.

Case 1 ($R=250\ \Omega$, range $0-V$): $V=I_g(G+250)$

Case 2 ($R=900\ \Omega$, range $0-3V$): $3V=I_g(G+900)$

Dividing: $\dfrac{3V}{V}=\dfrac{G+900}{G+250} \Rightarrow 3(G+250)=G+900$

$$3G+750=G+900 \Rightarrow 2G=150 \Rightarrow G=75\ \Omega$$

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