Question

A circuit consists of a large electromagnet that has an inductance of 52.0 H and a resistance of 8.00 ?, a dc 270 V power source, and an open switch - all connected in series.

A) How long after the switch is closed is the current equal to 10.5 A?

B) How long after the switch is closed is the current equal to 31.9 A?

Answer 1

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A circuit consists of a large electromagnet that has an inductance of 49.0 H and a resistance of 7.40 ?, a dc 250 V power source, and an open switch - all connected in series. How long after the switch is closed is the current equal to 10.8 A? How long after the switch is closed is the current equal to 31.8 A?

Inductance = L = 49 H

Resistance = R = 07.4 ohms

Voltage of power source = V = 250 V

Current in the circuit = i(t) = (V/R)( 1 - exp(-Rt/L))

a) i(t) = 10.8 = (250/7.4)( 1- exp(-7.4*t/49))

(10.8*7.4)/250 = 1 - exp(-7.4*t/49)

  exp(-7.4*t/49) = 1 - ( (10.8*7.4)/250)

t = - (49/7.4)*ln(1 - ( (10.8*7.4)/250))

t = 2.55 s

b)

  i(t) = 31.8 = (250/7.4)( 1- exp(-7.4*t/49))

(31.8*7.4)/250 = 1 - exp(-7.4*t/49)

  exp(-7.4*t/49) = 1 - ( (31.8*7.4)/250)

t = - (49/7.4)*ln(1 - ( (31.8*7.4)/250))

t = 18.77 s

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Time taken for the current equal to 10.8 A = 2.55 s

Time taken for the current equal to 31.8 A = 18.77 s