Answer to Question #201335 in Electrical Engineering for aman

Question #201335

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
Expert's answer
2021-06-01T03:46:06-0400

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

"110sin (20t + 30\u00b0) + 220cos (20t \u2014 90\u00b0) = 110\\angle\u2014 60\u00b0 + 220\\angle \u2014 90\u00b0"

"= 55\u2014 j95.26\u2014 j220 = 55\u2014 j315.26 = 320.02\\angle \u2014 80.1\u00b0"  

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

"30cos (5t + 60\u00b0) \u2014 20 sin (5t + 60\u00b0) = 30\\angle \u2014 30\u00b0 \u2014 20\\angle 60\u00b0"

"= 15 + j25.98 \u2014 17.321+ j10 = \u2014 2.321+ j35.98 = 36.05\\angle93.69\u00b0"

impedance



"Z=320\/36\\approx9 \\ (V)" 


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