Question

What do you mean by the current sensitivity of a moving coil galvanometer? Resistance of a galvanometer is \( 50 \, \Omega \) and for full-scale deflection, the current is \( 0.05 \, \mathrm{A} \). What would be the required length of a wire to convert it into an ammeter of 5 A range? (Area of cross-section of wire = \( 2.7 \times 10^{-6} \, \mathrm{m^2} \), specific resistance of the wire material = \( 5.0 \times 10^{-7} \, \Omega \cdot \mathrm{m} \))

Hint:

The shunt resistance determines the range of an ammeter. Use the formula \( S = \frac{IG \, G}{I - IG} \).

Answer 1

The shunt resistance is: \[ S = \frac{IG \, G}{I - IG}. \] Substituting \( G = 50 \, \Omega, I = 5 \, \mathrm{A}, IG = 0.05 \, \mathrm{A} \): \[ S = \frac{0.05 \times 50}{5 - 0.05} = 0.5 \, \Omega. \] The length of the wire is: \[ R = \rho \frac{l}{A} \quad \Rightarrow \quad l = \frac{R A}{\rho}. \] Substituting \( R = 0.5, A = 2.7 \times 10^{-6}, \rho = 5.0 \times 10^{-7} \): \[ l = \frac{0.5 \times 2.7 \times 10^{-6}}{5.0 \times 10^{-7}} = 2.7 \, \mathrm{m}. \]