Question

An AC voltage of the form ?v = 100 sin 345t where ?v is in volts and t is in seconds, is applied to a series RLC circuit. If R = 36.0 ?, C = 26.0 µF, and L = 0.250 H, find the following.

(a) the impedance of the circuit
???

(b) the rms current in the circuit
??A

(c) the average power delivered to the circuit
??W

Answer 1

Given , R = 36.0 ohms , C = 26.0 µF, and L = 0.250 H ,

w = 345 rad/s

Using,

Impedence of the circuit   Z = sqrt( R² + ( X_L - X_C)²)

X_L   = w* L = 345 * 0.25H = 86.25 ohms

X_C = 1 / w*C = 1 / 345* 26*10^-6F = 111.483 ohms

Z = sqrt( ((36)² + ( 86.25 - 111.483)²))

Z = 43.963 Ohms

b ) I_rms = V_rms / Z

V_rms = V _max / sqrt(2) = 100 / sqrt(2) = 70.71 V

I _rms   = 70.71 / 43.96 = 1.608 A

c ) Pavg = I²_rms *Z = ( 1.608 )² * 43.963

Pavg = 113.73 W