c
\(Z = \sqrt {{R^2} + {{\left( {\frac{1}{{2\pi \nu C}}} \right)}^2}} = \sqrt {{{(3000)}^2} + \frac{1}{{{{\left( {2\pi \times 50 \times \frac{{2.5}}{\pi } \times {{10}^{ - 6}}} \right)}^2}}}} \)

==> \(Z = \sqrt {{{(3000)}^2} + {{(4000)}^2}} = 5 \times {10^3}\Omega \)\(\cos \varphi = \frac{R}{Z} = \frac{{3000}}{{5 \times {{10}^3}}} = 0.6\)

\(P = {V_{rms}}{i_{rms}}\cos \varphi = \frac{{V_{rms}^2\cos \varphi }}{Z}\)

==> \(P = \frac{{{{(200)}^2} \times 0.6}}{{5 \times {{10}^3}}} = 4.8W\)