Question

Find the impedance of the circuit if supply voltage is v(t) =110sin(20t+30 )+220cos(20t-90 )V and the current i(t)=30cos(20t+60 )-20sin(20t+60 )A

Answer 1

Converting these sinusoids to the phasor domain to add them easily, 

$110sin (20t + 30°) + 220cos (20t — 90°) = 110\angle— 60° + 220\angle — 90°$

$= 55— j95.26— j220 = 55— j315.26 = 320.02\angle — 80.1°$  

Converting these sinusoids to the phasor domain to add them easily, 

$30cos (5t + 60°) — 20 sin (5t + 60°) = 30\angle — 30° — 20\angle 60°$

$= 15 + j25.98 — 17.321+ j10 = — 2.321+ j35.98 = 36.05\angle93.69°$

impedance

$Z=320/36\approx9 \ (V)$