c
Let \(r_{1}\) and \(r_{2}\) are the radius of coil \(1\) and \(2\). If \(B_{1}\) and \(B_{2}\) are magnetic induction at their centre, then

\(B_{1}=\frac{\mu_{0} I_{1}}{2 r_{1}} ;\) and \(B_{2}=\frac{\mu_{0} I_{2}}{2 r_{2}}\)

Since \(B_{1}=B_{2} ;\) and \(r_{1}=2 r_{2}\)

\(I_{1}=2 I_{2}\)

Again if \(R_{1}\) and \(R_{2}\) are resistance of the coil \(1\) and \(2\) then \(R_{1}=2 R_{2}(\) as \(R \propto\) length \(=2 \pi r)\) and if \(V_{1}\) and \(V_{2}\) are the potential difference across them respectively, then

\(\frac{V_{1}}{V_{2}}=\frac{I_{1} R_{1}}{I_{2} R_{2}}=\frac{\left(2 I_{2}\right)\left(2 R_{2}\right)}{I_{2} R_{2}}=4\)