Question

An RLC circuit with R = 23.5 Ω , L = 396 mH , and C = 49.5 μF is connected to an ac generator with an rms voltage of 29 V . (Part A) Determine the average power delivered to this circuit when the frequency of the generator is equal to the resonance frequency. Express your answer using two significant figures. (Part B) Determine the average power delivered to this circuit when the frequency of the generator is twice the resonance frequency. Express your answer using two significant figures. (Part C) Determine the average power delivered to this circuit when the frequency of the generator is half the resonance frequency. Express your answer using two significant figures.

Answer 1

Answer:

power  is 35.5 W

power is 1.06 W

power is 1.06 W

Explanation:

Given data

R = 23.5 Ω

L = 396 mH

C = 49.5 μF

voltage = 29 V

solution

we know that in 1st part power that is equal to square of current × R

so

power = I²R

so current I = V/Z = 29/23.5   because R = Z at resonance

current = 1.23 A

power = 1.23²×23.5

power = 35.5 W

and

in 2nd part we know that frequency that is

f = 1/2π × √(1/LC)

f = 1/2(3.14) × √(1/396×10^-3×49.5×10^-6)

f = 35.94 Hz

so power = I²R

here

I =   V/Z

Z = √( R² + (x - y)²)

x = 2π(2f) L

x = 2(3.14)× ( 2×35.94)×( 396×$10^{-3}$

x = 178.84 ohm

y = 1 / 2π(2f) C

y =  1  /  2(3.14)× ( 2×35.94)×( 49.5×$10^{-6}$

y = 44.73 ohm

so

Z = √( 23.5² + (178.84 - 44.73)²)  

Z = 136.15 ohm

so current = 29 / 136.15

current I = 0.212 A

so power = 0.212² / 136.15

power = 1.06 W

and

in 3rd part same like 2nd

frequency = 35.94  Hz and X = 2π(2f) L = 2(3.14)× ( 35.94/2)×( 396×$10^{-3}$

X = 44.71 ohm

Y = 1 / 2π(2f) C = 1 / 2(3.14)× ( 35.94/2)×( 49.5×$10^{-6}$

Y = 178.98 ohm

so Z = √( 23.5² + (44.71 - 178.98)²)

Z = 136.25 ohm

current = 29 / 136.25

current = 0.212 A

so power = 0.212² / 136.15

power = 1.06 W