A circuit connected to an \(ac\) source of \(emf\) \(e = e_0\, sin\, (1000t)\) with \(t\) in seconds, gives a phase difference of \(\frac{\pi }{4}\) between the \(emf\) \(e\) and current \(i\). Which of the following circuits will exhibit this?

\(\Rightarrow\) Reactance \((X)=\) Resistance \((R)\) Now by checking option.

Option \((A)\)

\(\mathrm{R}=1000 \,\Omega\) and \(\mathrm{X}_{\mathrm{c}}=\frac{1}{10^{-6} \times 100}=10^{4} \,\Omega\)

Option \((B)\)

\(\mathrm{R}=10^{3} \,\Omega\) and \(\mathrm{X}_{\mathrm{L}}=10 \times 10^{-3} \times 100=1 \,\Omega\)

Option \((\mathrm{C})\)

\(\mathrm{R}=10^{3} \,\Omega\) and \(\mathrm{X}_{\mathrm{L}}=10^{-3} 100=10^{-1}\, \Omega\)

Option \((D)\)

\(\mathrm{R}=10^{3} \,\Omega\) and \(\mathrm{X}_{\mathrm{c}}=\frac{1}{10 \times 10^{-6} \times 100}=10^{3} \,\Omega\)