A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε = V_a - V_b = ε_msinωt, where ε_m = 120 V and ω = 620 radians/second. The values for the remaining circuit components are: R = 53 Ω, C = 413 μF. The value for L is unkown. What is known is that the voltage across the generator leads the current in the circuit by φ = 64^o.

1) What is t₁, the first time after t = 0 when the magnitude of the voltage across the inductor is maximum?

2) What is Z, the impedance of the circuit?

3) What is L, the value of the inductor?

4) What is V_L,max, the magnitude of the maximum voltage across the inductor?

5) What is V_L = V_b - V_c, the voltage across the inductor, at time t = 0? Note that V_L is a signed number.

6) In order to make the votage across the generator become in phase with the current in the circuit (i.e., make the phase φ equal to zero), how would the value of C have to change, keeping all other circuit parameters the same?

The value of C would need to be decreased

The value of C would need to be increased.

It is impossible to bring the voltage across the generator in phase with the current in the circuit by only changing the value of C, keeping all other circuit parameters fixed.