In the figure, = 114 V, R 1 = 9.41 , R 2 = 20.4 , R 3 = 28.5 , and L = 2.48 H. I

Question

In the figure, = 114 V, R1 = 9.41 , R2 = 20.4 , R3 = 28.5 , and L = 2.48 H. Immediately after switch S is closed, what are (a) i1 and (b) i2? (Let currents in the indicated directions have positive values and currents in the opposite directions have negative values.) A long time later, what are (c) i1 and (d) i2? The switch is then reopened. Just then, what are (e) i1 and (f) i2? A long time later, what are (g) i1 and (h) i2?http://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c30/fig30_62.gif

Explanation / Answer

As I was not able to see the image, I tried looking for same type of question to get a description of the circuit,

When I am solving this question, I am making few assumptions: R3 and inductor are in series.

a) Immediately when the switch is closed,no current will flow through inductor ( it resists changes in current passing through it), therefore i1 = i2

The effective resistance =9.41 + 20.4 = 29.81

i1=i2= 114/ 29.81 = 3.824 A apprx

b) after a long time, ( post closing of switch) = the inductor behave like short circuit and offers no resitance,

therefore, parallel combination of R2 and R3 will be in series with R1

R23 =(20.4 x 28.5 )/ ( 20.4 + 28.5) = 581.4/ 48.9 = 12 ohms apprx

Req= 9.41 + 12= 21. 3 ohms apprx

I = 114/ 21.3 = 5.35 A

i 1= 5.35 A =---------it will divide into i2 and i3

voltage across R1 = 5.35 ( 9.41) = 50.63 V apprx'

Voltage drop across R2 = 114- 50.63= 63.63 V ap[rx

i2 = 63.63/ 20.4= 3.12 A pprx

i3 ( curent through R3 and Inductor) = 63.63/ 28.5 = 2.23 A

c) switch reopened again, i1 = 0 A ( as no cureent passes through R1)

but current will continue through inductor as its nature is to oppose the change in cureent

i3 = i2 = 2.23 A

d) after teh switch is closed for along time, all cureents will be 0

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