Answer to Question #182210 in Electric Circuits for Vin

Question

an e.m.f. represented by e=100 sin 100pi t is impressed across a circuit consisting of 40 ohms resistor in series with a 40microF capacitor and a 0.25 H indicator. Determine the r.m.s value of the current the power supplied the power factor.

Answer 1

Resistance, $R$ = $40$ $\Omega$

Inductance, $L=0.25 \space H$

Capacitance, $C=40\space\mu F=40\times10^{-6}\space F$

$\omega=100\pi$

$X_L=\omega L$ $=100\pi\times0.25=78.53$

$X_C=\dfrac{1}{\omega C}=\dfrac{1}{100\pi\times40\times10^{-6}}=79.57$

Impedance, $Z=\sqrt{R^2+(X_L-X_C)^2}=40.01\space\Omega$

Power factor, $cos\phi=\dfrac{R}{Z}=0.99$

$V_{RMS}=\dfrac{V_M}{2}=\dfrac{100}{2}=50\space V$

RMS value of current, $I_{RMS}=\dfrac{V_{RMS}}{Z}=\dfrac{50}{40.01}=1.24\space A$

Power Supplied, P$=I_{RMS}^2Zcos\phi=60.90\space W$