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Current Electricity

Question
CBSEENPH12039489

An inductor (L = 0.03 H) and a resistor (R = 0.15 kΩ) are connected in series to a battery of 15V EMF in a circuit shown. The key K1 has been kept closed for a long time. Then at t = 0, K1 is opened and key K2 is closed simultaneously. At t = 1 ms, the current in the circuit will be:
(straight e to the power of 5 space approximately equal to space 150)

  • 100 mA

  • 67 mA

  • 6.7 mA

  • 0.67 mA

Solution

D.

0.67 mA

After long time inductor behaves as short-circuit.
At t = 0, the inductor behaves as short circuit.The current,
straight I subscript 0 space equals space straight E subscript 0 over straight R space equals space fraction numerator 15 straight V over denominator 0.15 space kΩ end fraction space equals space 100 space mA
As K2 is closed, current through the indicator starts decay which is given at any time t as
straight I space equals space straight I subscript 0 straight e to the power of fraction numerator negative tR over denominator straight L end fraction end exponent space equals space left parenthesis 100 space mA right parenthesis space straight e to the power of fraction numerator negative tx 15000 over denominator 3 end fraction end exponent
straight t space equals space 1 space ms
straight I space equals space left parenthesis 100 mA right parenthesis straight e to the power of fraction numerator 1 space straight x space 10 to the power of negative 3 end exponent space straight x space 15 space straight x 10 cubed over denominator 3 end fraction end exponent
straight I space equals space left parenthesis 100 space mA right parenthesis straight e space equals space 06737 space mA space or space straight I space equals space 0.67 space mA