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The A.C. voltage and current in an L-C-R A.C. series circuit are given by the following expression V = 200 sqrt(2) cos ( 3000t - 55^(@) V, I = 10 sqrt(2) cos ( 3000 t - 10^(@) ) A. Calculate the impedance and the resistance of the above circuit. |
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Answer» Solution :`delta_(1) = 10^(@), delta_(2) = 55^(@)` `:. delta = delta_(2) - delta_(1) = 55^(@) - 10^(@) = 45^(@)` `V_(m) = 200 sqrt(2) V, I_(m) = 10sqrt(2) A` here, `delta= 45^(@)` `:. tan delta = tan 45^(@)` `:. tan delta=1 ` Now for L-C-R- series circuit, `:. tan delta = ( omega l- (1)/( omega C ))/(R )` `:. 1= ( omega L - ( 1)/( omega C ))/( R )` `R = omega L - ( 1)/( omega C )`....(i ) and `| Z | = sqrt( R^(2) + ( omega L - ( 1)/( omega C))^(2)) ` `= sqrt( R^(2) + R^(2))`[ `:. ` From result (i) ] `| Z | = sqrt( 2).R`....(ii) and `|Z | ( V_(m))/( I_(m))` `:. | Z | ( 200 sqrt(2))/( 10sqrt(2))` `:. | Z | = 20 Omega`....(III) From equation (ii) and (iii) `:. 20 = sqrt( 2) xx R ` `:. 10 sqrt(2) = R ` `:. 10 xx 1.414 = R ` `:. R = 14.14 Omega` |
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