5. Switch a in the circuit has been open for a long time and switch b has been closed for a long time. Switch a is closed at t = 0. After remaining closed for 1s, switches a and b are opened simultaneously and remain open indefinitely. Determine the expression for the inductor current i that is valid when (a) 0 ≤ t ≤ 1s and (b) t ≥ 1s

Question

Engineering

Xavier Cantrell

1 September, 18:57

5. Switch a in the circuit has been open for a long time and switch b has been closed for a long time. Switch a is closed at t = 0. After remaining closed for 1s, switches a and b are opened simultaneously and remain open indefinitely. Determine the expression for the inductor current i that is valid when (a) 0 ≤ t ≤ 1s and (b) t ≥ 1s

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Answers (1)

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Hayden Jones · Answer 1

(a) 1/L∫Vdt; integral t [0,1]

(b) 1/L∫Vdt; integral t [ 1, infinity]

Explanation:

An Inductor current I, flowing through an inductor depends on the voltage, V, across the inductor and the inductance, L, of the inductor. The switch 1, 2 timing varies the voltage V with time t

The expression for inductor current is given as:

I = 1/L∫Vdt,

where I is equal to the current flowing through the inductor, L is equal to the inductance of the inductor, and V is equal to the voltage across the inductor.

The formula can also be written as:

I = I0 + 1/L∫Vdt, where I is inductor current at time t, and io is inductor current at t = 0. Time can be varied by controlling the switch