1. In the figure shown below, source frequency is 500 rad/sec and current $I_2 = 1.25 \angle 60^\circ$ Amp.
Find,
a. Currents $I_1$ and $I_3$.
b. Source voltage $V_s$
c. Power factor of the entire circuit
d. Draw phasor diagram. Find magnitudes and positions of all the quantities.
2. An impedance (inductive) $Z_L = (11.5 + j10)$ ohms is connected in parallel with an impedance (capacitive) $Z_c = (8 - j20)$ ohms. Calculate (a) the conductance and susceptance of each branch; (b) the total conductance, susceptance, and admittance of the circuit; (c) the current in each branch, and the total current and power factor, if the impressed emf is 120 volts.
3. A coil of wire having a value of $(5 + j8)$ ohms is connected in series with a capacitive reactance $X_c$, and this series combination is then connected in parallel with a resistor R. If the equivalent impedance of the circuit is $4 \angle 20^\circ$ ohms, calculate the values of $X_c$ and R.