Question 207: AC fundamentals

Question

A series $\mathrm{LCR}$ circuit consists of $\mathrm{R}=80 \Omega, \mathrm{X}_{\mathrm{L}}=100 \Omega$, and $\mathrm{X}_{\mathrm{C}}=40 \Omega$. The input
voltage is 2500 $\cos (100 \pi \mathrm{t}) \mathrm{V}$. The amplitude of current, in the circuit, is _________ A.

Accepted Answer

$\omega=100 \pi$
$$
\begin{aligned}
& 	ext { So } Z=\sqrt{R^{2}+\left(X_{L}-X_{C}ight)^{2}} \\
& =\sqrt{80^{2}+(100-40)^{2}} \\
& =100 \Omega \\
& i_{0}=\frac{V_{0}}{Z}=\frac{2500}{100} \mathrm{~A}=25 \mathrm{~A}
\end{aligned}
$$

AC fundamentals

A series \mathrm{LCR} circuit consists of \mathrm{R}=80 \Omega, \mathrm{X}_{\mathrm{L}}=100 \Omega, and \mathrm{X}_{\mathrm{C}}=40 \Omega. The input voltage is 2500 \cos (100 \pi \mathrm{t}) \mathrm{V}. The amplitude of current, in the circuit, is _________ A.

Integer / Numeric Answer Type