Question

A moving coil galvanometer when shunted with \(2\,\Omega\) resistance gives a full scale deflection for a current of \(500\,\text{mA}\). When a resistance of \(470\,\Omega\) is connected in series it gives a full scale deflection for \(10\,\text{V}\) potential applied on it. The value of resistance of galvanometer coil is _____ \(\Omega\).

Answer 1

Correct Answer: 50

Concept: When a galvanometer of resistance \(G\) is shunted by resistance \(S\), the full scale current becomes \[ I = I_g\left(1+\frac{G}{S}\right) \] When a resistance \(R\) is connected in series, the potential required for full scale deflection is \[ V = I_g(G+R) \] Step 1: {Use the shunt condition.} Given \[ S=2\,\Omega \] \[ I=500\,\text{mA}=0.5\,\text{A} \] Thus \[ 0.5 = I_g\left(1+\frac{G}{2}\right) \] \[ I_g = \frac{0.5}{1+\frac{G}{2}} \] Step 2: {Use the series resistance condition.} \[ V=10\,\text{V},\quad R=470\,\Omega \] \[ 10 = I_g(G+470) \] Substitute \(I_g\): \[ 10 = \frac{0.5}{1+\frac{G}{2}}(G+470) \] Step 3: {Solve for \(G\).} \[ 10\left(1+\frac{G}{2}\right)=0.5(G+470) \] \[ 10+5G=0.5G+235 \] \[ 4.5G=225 \] \[ G=50\,\Omega \]