c
Resistance of series combination of \(3\,\Omega \) and \(1\,\Omega \) is

\(R_{1}=3+1=4 \,\Omega, R_{2}=8\, \Omega\)

Let \(i\) be the total current in the circuit.

Current through \(R_{1}\) is \(i_{1}=\frac{i \times R_{2}}{R_{1}+R_{2}}=\frac{i \times 8}{12}=\frac{2 i}{3}\)

Current through \(R_{2}\) is \(i_{2}=\frac{i \times R_{1}}{R_{1}+R_{2}}=\frac{i \times 4}{12}=\frac{i}{3}\)

Power dissipated in \(3\, \Omega\) resistor is

\(P_{1}=i_{1}^{2} \times 3\)       ....\((i)\)

Power dissipated in \(8 \Omega\) resistor is

\(P_{2}=i_{2}^{2} \times 8\)       ....\((ii)\)

\(\therefore \quad \frac{P_{1}}{P_{2}}=\frac{i_{1}^{2} \times 3}{i_{2}^{2} \times 8}\) or, \(\frac{P_{1}}{P_{2}}=\frac{(2 i / 3)^{2} \times 3}{(i / 3)^{2} \times 8}=\frac{12}{8}=\frac{3}{2}\)

\(P_{1}=\frac{3}{2} \times P_{2}=\frac{3}{2} \times 2=3 \,\text { watt }\)

\(\therefore\) Power dissipated across \(3 \Omega\) resistor is \(3\,watt.\)