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A moving-coil galvanometer of resistance G gives full-scale deflection for current I_g. It is converted (i) into an ammeter of range 0 to I₀ (with I₀ > I_g) using a shunt R_A, and (ii) into a voltmeter of range 0 to V (V = G I_g) using a series resistance R_V. Which relation holds?

1. R_A R_V = G² (I_g/(I₀ - I_g)) and R_A/R_V = ((I₀ - I_g)/I_g)²
2. R_A R_V = G² and R_A/R_V = (I_g/(I₀ - I_g))²
3. R_A R_V = G² and R_A/R_V = I_g/(I₀ - I_g)
4. R_A R_V = G² ((I₀ - I_g)/I_g) and R_A/R_V = (I_g/(I₀ - I_g))²

Correct answer: R_A R_V = G² and R_A/R_V = (I_g/(I₀ - I_g))²

Solution

R_A = G I_g/(I₀ - I_g) and R_V = G(I₀ - I_g)/I_g, so their product is G² and their ratio is (I_g/(I₀ - I_g))².

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