Question

An alternating e.m.f. of 0.2 V is applied across an LCR series circuit having R = 4 `Omega`, C = 80 µF and L = 200 mH. At resonance the voltage drop across the inductor is ____________.

पर्याय

• 2.5 V

• 5 V

• 1 V

• 10 V

Answer 1

An alternating e.m.f. of 0.2 V is applied across an LCR series circuit having R = 4 `Omega`, C = 80 µF and L = 200 mH. At resonance the voltage drop across the inductor is 2.5 V.

Explanation:

At resonance X_L = X_C

`therefore "Current" = 0.2/"R" = 0.2/4 = 0.1/2 = 0.05  "A"`

`"Now", "X"_"L" = omega"L" = 2pi "fL"`

`"f" = 1/(2pisqrt"LC")`

`therefore "X"_"L" = (2pi"L")/(2pisqrt"LC") = sqrt("L"/"C")`

`"X"_"L" = sqrt((200 xx 10^-3)/(80 xx 10^-6))`

`= 10^2/2`

`= 50  Omega`

`therefore "V"_"L"= "i" xx "L"`

`= 0.05 xx 50`

`= 2.5  "V"`