Question

An AC voltage of the form Δv = 100 sin 1 000t, where Δv is in volts and t is in seconds, is applied to a series RLC circuit. Assume the resistance is 350 Ω, the capacitance is 5.35 µF, and the inductance is 0.500 H. Find the average power delivered to the circuit.
W

Answer 1

Given :-

R = 350 ohm,

L = 0.500 H,

C = 5.35 uF = 5.35 x 10^-6 F

the voltage eqⁿ

V = 100 sin(1000 t)

where V_m = 100 volt and w = 1000 rad/s

P_avg = V_rms I_rms cosQ

then V_rms = V_m / sqrt(2) = 70.710 v

the total impedence

Z = sqrt [ R² + ( X_L - X_C )² ]

here X_L = wL = 1000 x 0.500 = 500 ohm

X_C = 1 / wC = 1 / (1000 x 5.35 x 10^-6) = 186.91 ohm

Z = sqrt[ (350)² + ( 500 - 186.91 )² ]

Z = 469.68 ohm

so the current

I_m = V_m / Z = 100 / 469.68 = 0.2129 Amp

so I_rms = I_m / sqrt(2) = 0.151 Amp

cosQ = R / Z = 350 / 469.68 = 0.745

so the average power

P_avg = 70.710 x 0.2129 x 0.745

P_avg = 11.215 W