Shown below is an LRC circuit connected to an AC generator with R = 14 ?, XL = 4

Question

Shown below is an LRC circuit connected to an AC generator with R = 14 ?, XL = 40 ?, and XC = 11 ?.

The generator voltage oscillates at a frequency of 60 Hz.

The maximum current in the circuit is measured to be 0.8 A

current in the circuit the moment the generator voltage is at max: 0.35A.

1) The current through the capacitor _____ the voltage across the capacitor and the current through the resistor _____ the voltage across the resistor.

a) leads, lags

b) lags, leads

c) leads, is in phase with

d) is in phase with, is in phase with

2)The frequency is changed to now be at the resonant frequency of the circuit (but the voltage of the generator stays the same). What is the maximum current in the circuit?

please help me solve above questions with explanations!

Explanation / Answer

V = V0Sin(wt)

Voltage will be Max when t = 0

Maximum Current will be at resonance

Maximum Current = V/R

0.8 = V/14

Therefore

Vmax = 11.2 V

So Current = Vmax/(R^2 + (XL -Xc)^2)

= 11.2/sqrt(14^2 + (40-11)^2)

= 0.35 A

c) leads, is in phase with

At Resonance

Max Current = Vmax/R

= 11.2/14

= 0.8 A

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