In the figure, take ? 0 = 12 V , R = 2.3 ? , and L = 20 H . Initially the switch

Question

In the figure, take ?0 = 12V , R = 2.3? , and L = 20H . Initially the switch is in position B and there's no current anywhere. At t = 0 the switch is thrown to position A, and at t = 13.0s it's returned to B.(Figure 1)

In the figure, take ?0 = 12V , R = 2.3? , and L = 20H . Initially the switch is in position B and there's no current anywhere. At t = 0 the switch is thrown to position A, and at t = 13.0s it's returned to B.(Figure 1) Find the inductor current at t = 6.50s Find the inductor current at t = 19.5s .

Explanation / Answer

PART A:

writing the KVL equation for the loop,

V-ir- Ldi/dt=0

or i=io*(1-e^(-RT/L))

where io=12/2.3

=5.217 A

so, i(t)=5.217*(1-e^(-0.115*t))

so,

i(6.5)=2.746 A

PART B :

now the circuit is discharging,

I=io(e^(-0.115*t)

but here io=2.746

so,

i=2.746*e^(-0.115*(19.5-16))

=1.3 A

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