Saved Bookmarks
| 1. |
The A.C. voltage and the current in a circuit are given by the following expressions. V=110sqrt2 cos (2000t + 25^@)V and I = 10sqrt2 cos (2000t - 20^@)A. Calculate impedance and resistance of the circuit. |
|
Answer» 7.679 `Omega` `V_m=110sqrt2V` `I_m=10sqrt2A` `omega`=2000 rad/s `delta=delta_2-delta_1=20^@-(-25^@)=45^@` Fro L-C-R series circuit `TAN delta=(omegaL-1/(OMEGAC))/R` `tan45^@ = (omegaL-1/(omegaC))/R` `therefore R=omegaL-1/(omegaC)`....(1) `[because tan45^@=1]` Now, `|Z| = sqrt(R^2+(omegaL-1/(omegaC))^2)` `=sqrt(R^2+R^2)` [From (1)] `therefore |Z|=sqrt2R` ...(2) But `|Z|=V_m/I_m=(110sqrt2)/(10sqrt2)=11Omega` `therefore` From EQUATION (2), `|Z|=sqrt2R` `11=sqrt2R` `therefore R=11/sqrt2` `=11/1.414` `therefore R=7.779 Omega` |
|