Question

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 = 231 radians/second. The inductance L = 155 mH. The values for the capacitance C and the resistance R are unkown. What is known is that the current in the circuit leads the voltage across the generator by φ = 49 degrees and the average power delivered to the circuit by the generator is P_avg = 106 W.

What is I_max, the amplitude of the current oscillations in the circuit?

What is R, the value of the resistance of the circuit?

What is C, the value of the capacitance of the circuit?

The value of ω is now changed, keeping all other circuit parameters constant, until resonance is reached. How was ω changed?

ω was decreased

ω was increased

What is the average power delivered to the circuit when it is in resonance?

Answer 1

Solution :

part a : Determination of I_max :

part b : Determination of the value of Resistor, R:

Part c: Determination of value of Capacitance,C:

Hence, C = 27.03 and
          C = 60.58

Part d:

When the current is lagging behind the voltage, the capacitance,C of the circuit must increase in order to reach resonance.

where ω is decreasing.

When the current is leading the voltage, the inductance of the circuit, L must increase in order to reach resonance.

where, ω is increasing.

Part e : Determination of average power :