Question

1. Determine the current in the circuit by calculating the current in the resistor. Note: We will use I (and V_R since it has the same phase) for reference throughout our analysis (V_R/R = I).

2. Determine the capacitance of the circuit from its reactance, the current calculated above, and the frequency of the source (V_C/I = X_C).

3. Determine the inductance of the circuit from three different voltage measurements, the current calculated in step 1, and the frequency of the source, following the instructions below carefully (this can be complicated).

1. Determine the phase of V_LR with respect to V_R using the law of cosines (V_Lr²= V_LR² + V_R² – 2V_LRV_R cos(α)).

2. Determine the fraction of V_LR due to V_L alone (V_L = V_LRsin(α)).

3. Determine the inductance of the circuit from its reactance using the current determined in step 1 and the V_L determined above (V_L/I =X_L).

4. Determine the loss in the inductor and write it as a resistance using the current found in step 1

            (V_r = V_LRcos(α) – V_R and r = V_r/I).

4. Determine the phase between the source voltage and the current (φ = tan^-1 [(V_L – V_C)/(V_R+V_r)]).

5. Calculate the resonant frequency of the circuit from the values you determined for L and C

f (Hz)	R (ohms)	Vsource (V)	Vc (V)	VLr (V)	VLR (V)	VR (V)
0.5	10	10	1.0	10	10	3.5
1.5	10	10	0.1	10	10	1.

Answer 1