b
Total initial resistance \(=R_{G}+R_{1}=(50+2950)\, \Omega=3000\, \Omega\)

\(\varepsilon=3\, \mathrm{V}\)

\(\therefore\) Current \(=\frac{3\, \mathrm{V}}{3000 \,\Omega}=1 \times 10^{-3} \,\mathrm{mA}\)

If the deflection has to be reduced to \(20\) divisions, current \(i=1\, \mathrm{mA} \times \frac{2}{3}\) as the full deflection scale for

\(1\,\mathrm{mA}=30\) divisions.

\(3\, \mathrm{V}=3000\, \Omega \times 1 \,\mathrm{mA}=x\, \Omega \times \frac{2}{3} \,\mathrm{mA}\)

\(\Rightarrow x=3000 \times 1 \times \frac{3}{2}=4500\, \Omega\)

But the galvanometer resistance \(=50\, \Omega\)

Therefore the resistance to be added

\(=(4500-50) \,\Omega=4450\, \Omega\)