Exercise 30.23 Part A Find the initial rate of increase of current in the circui

Question

Exercise 30.23 Part A Find the initial rate of increase of current in the circuit. SubmitMyAnswersGiveUp Part B SubmitMyAnswersGiveUp Part C SubmitMyAnswersGiveUp Part D Find the final steady-state current. SubmitMyAnswersGiveUp Exercise 30.23 An inductor with an inductance of 2.60and a resistance of 7.30is connected to the terminals of a battery with an emf of 6.50and negligible internal resistance. Part A Find the initial rate of increase of current in the circuit. = SubmitMyAnswersGiveUp Part B Find the rate of increase of current at the instant when the current is 0.540. = SubmitMyAnswersGiveUp Part C Find the current 0.280after the circuit is closed. = SubmitMyAnswersGiveUp Part D Find the final steady-state current. = SubmitMyAnswersGiveUp

Explanation / Answer

V = 6.5V

R = 7.30

L = 2.6H

current in a series R-L circuit is given by

I = Io (1 - exp(-t/) )

here Io = steady state current = V/R = 6.50/7.3 = 0.89 A

and = L/R = 2.6/7.3 = 0.3562 s

=> I(t) = 0.89( 1-exp(-t/0.3562) ) A

rate of increase of current, r(t) = dI/dt = 0.89 (1/0.3562) exp(-t/0.3562) A/s

=> r(0) = 0.89 (1/0.3562) = 2.4986 A/s

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