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# Answer to Question #199847 in Electrical Engineering for A jaif

Question #199847

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

1
2021-05-31T06:39:41-0400

Converting the sinusoids to the phasor domain,

"110sin (20t + 30\u00b0) + 220cos (20t \u2014 90\u00b0)"

"110\\angle -60\u00b0 + 220\\angle- 90\u00b0"

"55 \u2014 j95.26 \u2014 j220"

"55 \u2014 j315.26"

"320.02\\angle \u2014 80.1\u00b0"

"v = 320.02cos (20t \u2014 80.11\u00b0) V"

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

"30cos (20t + 60\u00b0) \u2014 20 sin (20t + 60\u00b0)"

"30 \\angle\u2014 30\u00b0 \u2014 20 \\angle 60"

"15 + j25.98 \u2014 17.321+ j10"

"-2.321 +j35.98"

"36.05 \\angle93.69\u00b0"

Converting the result to the time domain,

"i = 36.05cos (5t + 93.69\u00b0) A"

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