Question

IV The expressions for the steady-state voltage and current at the terminals of the circuit shown below are Vg-300 cos(5000t+78"N , i,-6 sin(5000t+ 1 23°) A Circuit (a) What is the impedance seen by the source? (b) By how many microseconds is the current out of phase with the voltage?

Answer 1

Given, v_g = 300 cos(5000 pi t + 75 degree) v i_g = 6 sin(5000 pi t + 123 degree) A = 6 cos(5000 pi t + 123 degree - 90 degree) implies i_g = 6 cos(5000 pi t + 33 degree)A (a) Impedance, z = v_g/i_g = 300 angle 78 degree/6 angle 33 degree = 50 angle 45 degree ohm implies z = 35.35 + j 35.35 ohm (b) here, w = 5000 pi = 2 pi f implies f = 2500 H z implies Time period, T = 1/f = 400 mu Sec 1 cycle = 360 degree rightarrow 400 mu sec phase difference, = 45 degree rightarrow x mu sec implies x = 45 degree/360 degree times 400 mu sec implies x = 50 mu sec