Problem 31.58 An L-R-C series circuit has R = 50.0 , L = 0.700 H , and C = 7.00×

Question

Problem 31.58 An L-R-C series circuit has R = 50.0 , L = 0.700 H , and C = 7.00×104 F . The ac source has voltage amplitude 80.0 V and angular frequency 110 rad/s . Part A What is the maximum energy stored in the inductor? Express your answer to three significant figures and include the appropriate units. UL = SubmitMy AnswersGive Up Part B When the energy stored in the inductor is a maximum, how much energy is stored in the capacitor? Express your answer to three significant figures and include the appropriate units. UC = SubmitMy AnswersGive Up Part C What is the maximum energy stored in the capacitor? Express your answer to three significant figures and include the appropriate units. UC =

Explanation / Answer

Part A What is the maximum energy stored in the inductor?
Part B When the energy stored in the inductor is a maximum, how much energy is stored in the capacitor?
Part C What is the maximum energy stored in the capacitor?

Total Energy is constant !!

Max Energy stored in the Inductor, U = 1/2 * Li^2
Max Energy stored in the Capacitor, U = Q^2/2C

I = V/Z
V = 80.0 v
Z = sqrt(R^2 + (XL-XC)^2)
Z = sqrt(50.0^2 + ( (110*0.7) - 1/(110*7.0*10^-4) )^2 )
Z = 81.23

I = 80.0/81.23 = 0.985 A

(A) Max Energy stored in the Inductor, U = 1/2 * 0.7 * 0.985^2
U = 0.34 J

(B) Energy stored in the capacitor, = 0.
(C) Maximum energy stored in the capacitor, U = 0.34 J

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