Question

A 10.5- resistor, a 15.9-μF capacitor, and a 15.2-mH inductor are connected in series with a 203-V generator. (a) At what frequency is the current a maximum? (b) What is the maximum value of the rms current? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

Answer 1

Answer:

(a) Frequency at which current is maximum is 323.9 Hz

(B) Maximum current in the circuit is 19.333 A

Explanation:

We have given resistance R = 10.5 ohm

Capacitance $C=15.9\mu F=15.9\times 10^{-6}F$

Inductance $L=15.2mH=15.2\times 10^{-3}H$

(a) Current is maximum when impedance will be minimum and impedance is minimum when there is condition of resonance.

At resonance $X_C=X_L$

$\frac{1}{\omega C}=\omega L$

$\omega ^2=\frac{1}{15.9\times 10^{-6}\times 15.2\times 10^{-3}}$

$\omega =2034.13$

$2\pi f =2034.13$

f = 323.9 Hz

(b) Current will maximum when resonance occurs at resonance impedance of the circuit is equal to resistance.

Voltage is given V = 203 volt

So maximum current $i=\frac{203}{10.5}=19.333A$