Find the value of C in the circuit shown in Fig. P8.21 so that Z is purely resistive at a...

Refer to Figure \(\mathrm{P} 8.16\) in the textbook.

Determine the impedance of inductor.

$$ \begin{aligned} Z_{L} &=j \omega L \\ &=j(2 \pi f) L \end{aligned} $$

Substitute \(60 \mathrm{~Hz}\) for \(f, \quad 5 \times 10^{-3} \mathrm{H}\) for \(L\).

$$ \begin{aligned} Z_{L} &=j(2 \pi(60))\left(5 \times 10^{-3} \mathrm{H}\right) \\ &=j 1.885 \Omega \end{aligned} $$

Determine the impedance of capacitor.

$$ \begin{aligned} Z_{C} &=\frac{1}{j \omega C} \\ &=\frac{1}{j(2 \pi f) C} \end{aligned} $$

Substitute \(60 \mathrm{~Hz}\) for \(f\).

$$ \begin{aligned} Z_{C} &=\frac{1}{j(2 \pi(60)) C} \\ &=\frac{2.65 \times 10^{-3}}{j C} \Omega \end{aligned} $$