(10% Problem 3: A resistor and inductor are comected to a 9.0 V battery by a swi

Question

(10% Problem 3: A resistor and inductor are comected to a 9.0 V battery by a switch as shown. The moment the switch is closed, curent flows through the circuit. The resistor has a resistance of R 380 S2 and the inductor has an inductance of L 312 mH. Randomized Variables 9.0V 380 125 Otheexpertta.com 20% Part (a At time t 0 the switch is closed and current flows through the circuit. The current increases with time and eventually reaches a steady state value of i Calculate the maximum curent imm in units of milliamps. Grade Summary 4 5 6 Attempts remaining 3 cotan0 asun0 atano acotano sinh0 cosh0 tanho cotanho Degrees Feedback: S deduction per feedback Hints: deduction per hit Hints remaining 2 Submission History Totals Auswer Feedback Totals 20% Part (b) Calculate the time constant, r, of the circuit in seconds. t, 20% Part (c) Write an equation that relates the current as a function of time i(r to the maximum curr imar. Express the equation in terms of imm and a, where a 3-tt. 20% Part (d) Determine the time, in seconds, at which the current has a value of i(tyo) 50% of i 20% Part (e) Determine the time, in seconds, at which the current has a value of i roo 99% of i

Explanation / Answer

here,

Resistance, R = 380 ohms
Inducatnce, L = 0.125 H

Part A:
Imax = V/R = 9/380 = 0.024 A

Part B:
Time Constant, tao = L/R = 0.125/380 = 3.289*10^-4 s

Part C:
I(max) = I(t)(1 - e(alpha)) ----------------(1)

Where, alpha = time/tao = t/tao

Part D:
From eqn 1 ,
0.5 = (1 - e(t/(3.289*10^-4)))
t = 6.049 s

Part E:
From eqn 1 ,
0.99 = (1 - e(t/(3.289*10^-4)))
t = 1.2099 s

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