Question

The difference in phases of the currents $i_1$ and $i_2$, when switch $S_1$ and $S_2$ are closed is

• A. 37º
• B. 53º
• C. 90º
• D. 60º

Answer 1

Answer: (C)

90º

Answer 2

1. Upper branch (R2 in series with L = 18 mH):

   Impedance: $Z_1 = R_2 + j\omega L = 12 + j(500 \cdot 0.018) = 12 + j9$

   Phase angle: $\phi_1 = \arctan(9/12) \approx 36.87^\circ$

2. Lower branch (R3 in series with C = 125 μF):

   First, compute the capacitive reactance: $X_C = \frac{1}{\omega C} = \frac{1}{500 \cdot 125 \times 10^{-6}} = 16 \, \Omega$

   Impedance: $Z_2 = R_3 - jX_C = 12 - j16$

   Phase angle: $\phi_2 = \arctan(-16/12) \approx -53.13^\circ$

3. Phase difference:

   $\Delta\phi = \phi_1 - \phi_2 = 36.87^\circ - (-53.13^\circ) = 90^\circ$