A voltmeter of resistance Rᵥ and an ammeter of resistance Rₐ are connected as shown in an attempt to measure the resistance R. The measured value of the resistance is Rₘ = V/I₀ where V is reading of voltmeter and I₀ is reading of the ammeter. Find the true value of the resistance in terms of Rₘ, Rᵥ and Rₐ.

Question

G1 Physics · Accepted Answer

Image The voltmeter is connected across R and draws current. Thus the ammeter reads total current through R parallel Rᵥ, so Rₘ = R||Rᵥ. Hence 1/Rₘ = 1/R + 1/Rᵥ, giving R = Rₘ Rᵥ/(Rᵥ - Rₘ).