A resistance R , capacitance C , and inductance L are connected in series to a v

Question

A resistance R, capacitance C, and inductance L are connected in series to a voltage source with amplitude Vand variable angular frequency .

Part A

If =0, the resonance angular frequency, find the maximum current in the resistor.

Express your answer in terms of the variables R, C, L, and V.

VR

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Correct

Part B

Find the maximum voltage across the capacitor.

Express your answer in terms of the variables R, C, L, and V.

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Incorrect; Try Again; 4 attempts remaining

Part C

Find the maximum voltage across the inductor.

Express your answer in terms of the variables R, C, L, and V.

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Part D

Find the maximum energy stored in the capacitor.

Express your answer in terms of the variables R, C, L, and V.

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Part E

Find the maximum energy stored in the inductor.

Express your answer in terms of the variables R, C, L, and V.

VR

Explanation / Answer

a)

at resonance , XL = Xc

hence z = R

so imax = maximum current = V/R

b)

Xc = capacitive reactance = 1/Wo C

Vcmax = maximum Voltage across the capacitor = imax Xc = (V/R) (1/Wo C) = V/(CWoR)

c)

XL = capacitive reactance = Wo L

VLmax = maximum Voltage across the inductor = imax XL = (V/R) (Wo L) = VLWo/R

d)

Emaxc = maximum energy stored in capacitor = (0.5) C V2cmax = (0.5) C V2/(CWoR)2 = (0.5) V2 /(C Wo2 R2)

e)

EmaxL = maximum energy stored in inductor = (0.5) L i2max = (0.5) L V2/(R)2

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