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  • When 100 V D. C. is applied across a solenoid a current of 1 A flows in it. When 100 V A. C. is applied across the same coil, the current drops to 0.5 A. If the frequency of the A. C. source is 50

When 100 V D. C. is applied across a solenoid a current of 1 A flows in it. When 100 V A. C. is applied across the same coil, the current drops to 0.5 A. If the frequency of the A. C. source is 50 Hz the impedance and inductance of the solenoid are

Option: 1

\mathrm{100\; \Omega, 0.93\; \mathrm{H} }


Option: 2

\mathrm{200\: \Omega, 1.0\: \mathrm{H} }


Option: 3

\mathrm{100 \: \Omega, 0.86 \: \mathrm{H} }


Option: 4

\mathrm{ 200 \Omega, 0.55 \mathrm{H}}


Answers (1)

best_answer

\mathrm{\begin{aligned} & R=V / I=100 / 1=100 \Omega \text { for } \mathrm{DC} \\ & \text { for AC } V=I \sqrt{R^2+\left(\omega^2 L^2\right)} \\ & \therefore \quad 100=0.5 \sqrt{R^2+\left(\omega^2 L^2\right)} \quad \text { or } 200=\sqrt{R^2+4 \pi^2 f^2 L^2} \\ & \text { or } \quad 200=\sqrt{100^2+4 \pi^2 \times(50)^2 \times L} \end{aligned}}

\mathrm{\text { Hence } L=0.55 \mathrm{H} \text { and } X=200 \Omega}

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Ritika Harsh

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