Question

A 63 ohm resistor and a 8.0 microF capacitor are connected in series to an ac source. (a) Calculate the impedance of the circuit if the source frequency is 54 Hz. (b) Calculate the impedance of the circuit if the source frequency is 5.4 MHz. Express your answer using two significant figures.

Answer 1

Resistor R = 63 $\Omega$ , Capacitor = 8.0 uF

Impedance, Z of an series cricuit with resistror and capacitor, $Z=\sqrt{R^2+X^{2}$ where X is reactanceof capacitor given as $X=1/\omega C=1/2\pi fC$ , f is frequency, C is capacitor.

(a) For f = 54 Hz, Putting the values of all the parameters in formula of Z we get , Z = 373.94 $\Omega$

(b) For f = 5.4 MHz, Putting the values of all the parameters in formula of Z we get , Z = 63.00 $\Omega$

Answer 2

Answer 3

$a)\\ Z = R + \frac{1}{j\omega C}\\ = 63 - \frac{j}{8 * 10^{-6} * 54 * 2 \pi}\\ \\ = 63 - j368.41\\ \\ |Z| = 373.75 ohms\\ \\ b\\ Z = R + \frac{}{j\omega C}\\ = 63 - \frac{j}{8 * 10^{-6} * 5.4 *10^{6} * 2 \pi}\\ \\ = 63 - j0.0037\\ \\ |Z| = 63 ohms$