R1 Rs i2 R2 L I Fig Q2 Fig Q3 Q3 In Fig Q38 100V R1100 R220

R1 Rs i2 R2 L I. Fig Q2 Fig Q3 Q3. In Fig Q38 =100V, R1=10.0 , R2-20.0 , R3-30.0 , and L-2.00H. Immediately after switch S is closed, what are (a) i1, and 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 (b) i, and i2? The switch is then reopened. Just then, what are (c) i1, and i2? A long time later, what are (d) i1, and i2?

Solution

a) suddenly when switch is closed the inductor acts as open circuit

R3 becomes obsolete

net R = R1 + R2 = 30 ohm

I1 = 100 / 30 = 3.33 A as inductor open circuit so the whole I1 flows as I2

I2 = I1 = 3.33 A

b) after a long time after switch is closed the inductor becomes shortcircuit

so R = R1 + R2|| R3 = 10 + 12 = 22 ohm

I1 = 100 / 22 = 4.55 A

using potential divider method current through R2 = R3/(R2+ R3) x I1 = 30/50 x 4.55 = 2.73 A

therefore I2 = 2.73A

c) as switch is opened the whole circuit becomes open circuit so I1 = 0

but the inductor acts as energy source so the current flowing through inductor just before the switch opened = current flowing through R2 in opposite direction = 4.55 - 2.73 = 1.82 in opposite direction

d) after a long tme i1 =0 12 =0 as circuit is open