Q1 A solenoid having an inductance of 9.19 H is connected in series with a 1.59

Question

Q1 A solenoid having an inductance of 9.19 H is connected in series with a 1.59 k resistor. (a) If a 20.0 V battery is connected across the pair, how long will it take in seconds for the current through the resistor to reach 77.2% of its final value? (b) What is the current through the resistor at a time t = 1.00L?

Q2 A coil with an inductance of 2.6 H and a resistance of 8.9 is suddenly connected to an ideal battery with = 77 V. At 0.15 s after the connection is made, what is the rate at which (a) energy is being stored in the magnetic field, (b) thermal energy is appearing in the resistance, and (c) energy is being delivered by the battery?

Explanation / Answer

1) a) time constant T = L / R

= 9.19 * 10-6 / 1.59 * 103 = 5.78 * 10-9 s

I = I0 (1 - e-t/T)

0.772 = (1 - e-t/T)

0.228 = e-t/T

t = -T * ln 0.228 = 5.78 * 10-9 * 1.478

time required = 8.54 * 10-9 s

b) I = I0 (1 - e-t/T)

I = E/R * (1 - e-t/T)

I = 20/(1.59 * 103) * (1 - e-t/T)

I = [ 20 / (1.59 * 103)] * (1 - e-1)

I = 7.95 * 10-3 A

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