Question

Find VAB in the circuit below. The two AC supply voltages have a frequency of 1kHz and are in phase. All resistances values are in ohms.

QUESTION TWO (20 MARKS) Find VAB in the circuit below. The two AC supply voltages have a frequency of 1KHZ and are in phase. All resistances values are in ohms. A 4 3mH 12 6 12V 32 V

Answer 1

j times L = j 2 pi F_L = j 18.84 ohm apply nodal analysis at V_A V_A - 32/4 + V_A/12 + V_A - V_B/j 18.84 ohm = 0 V_A(1/4 + 1/12 + 1/j 18.84) - V_B/+ j 18.34 = 8 (0.333 - j 0.053)V_A + j 0.053 V_B = 81 equation (1) apply nodal analysis at V_B V_B - 12/6 + V_B/6 + V_B - V_A/j 18.84 = 0 V_B(1/6 + 1/6 + 1/j 18.84) - V_A/j 18.84 = 2 (0.333 - j 0.053)V_B + j 0.053 V_A = 2 equation (2) \r\n from eq (2) V_B = 2 - j 0.053 V_A/(0.333 - j 0.053) substitute V_B in eq (1) (0.333 - j 0.053)V_A + j 0.053(2 - j 0.053 V_A/0.33 - j 0.053) = 8 (0.341 - j 0.051)V_A + (-0.049 + j 0.31) = 8 V_A = 8 - (-0.049 + j 0.31)/0.341 - j 0.051 V_A = 23.22 + j 2.563 substitute V_A value
i solve this problem by nodal analysis