For one series LCR A.C. circuit, voltages across L, C and R are each 10 V. Now, if only resistance is made half, new voltages across L, C and R will be .....,.... and ... respectively.

Options

A. 10 V , 10 V and 5 V
B. 10 V , 10 V and 10 V
C. 20 V , 20 V and 5 V
D. 20 V , 20 V and 10 V

Answer

D

Explanation

At time of resonance , Z=min. =R and so `I=V/R=V/R rArr V=IR` =10 volt (given) =`V_R` Also `V_L=IX_L` =10 Volt and `V_C=IX_C`=10 Volt
Now, after making resistance half , `R.=R/2` . Hence, new current in the resonance condition is ,
`I.=V/(Z.)=V/(R.)=V/(R//2)=(2V)/R=2I`
(i)`V._R=I.R.=(2V)/RxxR/2 =V` = 10 Volt
(ii)`V._L=I.X_L=(2I)(X_L)=2V_L`=20 Volt
(iii) `V._C=I.X_C=(2I)(X_C)=2V_C`= 20 Volt