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An inductor X(L) = 2Omega ) , a capacito...

An inductor `X_(L)` = 2`Omega` ) , a capacitor (`X_(C)` = 8`Omega`) and a resistance (R = 8 `Omega` ) are connected in series with an AC source . The voltage output of AC source is given by V = 10 cos(100`pi`t)
The instantaneous potential difference between points A and B, when the applied voltage is 3/5th of the maximum value of applied voltage is

A

0 V

B

6 V

C

8 V

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Z = `sqrt (R^(2) + (X_C - X_L)^(2)) = 10Omega`
cos `phi = R/Z = 4/5`
`therefore phi = 37^(@)`
`I_0 = V_0 / Z = 10/10 = 1A`
`I = 1cos(100pit + 37^(@))`
`V = 10 cos (100pit)`
The applied voltage is `3/5` th of the maximum applied voltage when , or `100 pit = 53^(@)`
`thereforeI = 1cos(53^(@)+ 37^(@)) = 0`
`therefore V_AB = V_"applied" = 3/5 xx 10 = 6V`
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