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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 ____________.
Options
2.5 V
5 V
1 V
10 V
MCQ
Fill in the Blanks
Solution
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 XL = XC
`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"`
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