CORRECT ANSWER IS 3.05 PLEASE SHOW ME HOW TO GET THIS ANSWER A battery of 32 vol

Question

CORRECT ANSWER IS 3.05

PLEASE SHOW ME HOW TO GET THIS ANSWER

A battery of 32 volts is connected in series to a 36 milli-henrie inductor and a 14 ohm resistor. 10.7 milli-seconds after the battery is connected it is removed. What is the voltage across the inductor 6 milli-seconds after the battery has been removed from the circuit? Answer in volts.

A battery of 32 volts is connected in series to a 36 milli-henrie inductor and a 14 ohm resistor. 10.7 milli-seconds after the battery is connected it is removed. What is the voltage across the inductor 6 milli-seconds after the battery has been removed from the circuit? Answer in volts.

3.05 ± 10%

Explanation / Answer

Given,

V = 32 Volts ; L = 36 x 10-3 H ; R = 14 Ohm

Current in circuit in t = 10 ms = 10.7 x 10-3 s will be given by:

I = V/R ( 1 - e-tR/L)

I = 32/14 ( 1 - e-10.7x10-3 x 14/36 x 10-3) = 2.286 ( 1 - 0.0156) = 2.25 A

The max Voltage after removing the battery will be, Vmax = I x R = 2.25 x 14 = 31.5 Volts

Now the voltage across inductir after 6 ms = 6 x 10-3 s will be:

VL = Vmax e-tR/L

VL = 31.5 x e-6 x 10-3 x 14/36 x 10-3 = 3.05 Volts

Hence, the voltage across inductor will be VL = 3.05 Volts.

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