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 the sinusoids to the phasor domain, 

$110sin (20t + 30°) + 220cos (20t — 90°)$

$110\angle -60° + 220\angle- 90°$

$55 — j95.26 — j220$

$55 — j315.26$

$320.02\angle — 80.1°$

$v = 320.02cos (20t — 80.11°) V$

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

$30cos (20t + 60°) — 20 sin (20t + 60°)$

$30 \angle— 30° — 20 \angle 60$

$15 + j25.98 — 17.321+ j10$

$-2.321 +j35.98$

$36.05 \angle93.69°$

Converting the result to the time domain, 

$i = 36.05cos (5t + 93.69°) A$