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An Inductor of 5 mh is Connected in Series
By BYJU'S Exam Prep
Updated on: September 25th, 2023
An inductor of inductance 5 mH is connected in series with 20 resistors and a battery of EMF 2 V, then the current through the circuit 10 msec after the switch is on is _________.
Fill in the blank with the correct answer.
Answer: 100 mAmp
An inductor of inductance 5 mH is connected in series with 20 resistors and a battery of EMF 2 V, then the current through the circuit 10 msec after the switch is on is 32.96 mAmp
100 mAmp
Solution:
Given,
Inductance L=5 mH,
Resistance R=20 Ohm,
E=2 V
At the instant t=0+(the instant just after the switch is closed), the inductor behaves as open circuit,
So, current through circuit I(0+)=I(0)=0 A
At the instant t=∞, inductor will act as short circuit, as the applied voltage is dc,
So current through the circuit I(∞)=E/R=2/20=0.1 A
The complete response of RL circuit I(t)=i(∞)+[i(0)-i(∞)]e-t/τ
Here, time constant τ=L/R=5mH /20 =0.25 msec
So, I(t)=0.1+[0-0.1]e-t/(0.25ms)
Then, current through inductor at t=10 msec is I(10 msec)=0.1+[0-0.1]e-(40)
I(10 msec)=100 mAmp
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