Shown below are three circuits with identical batteries, inductors, and resistor

ID: 778357 • Letter: S

Question

Shown below are three circuits with identical batteries, inductors, and resistors.

a) Rank the circuits, greatest first, according to the current through the resistor labeled R immediately after the switch is closed.

b) Repeat for a long time after the switch is closed.

c) Rank the circuits according to the current through the inductors a long time after the switch is closed.

d) Rank the circuits by current through R just after the switch is reopened a long time later.

e) Rank by current through R a long time after it is reopened.

I believe a) is 1=2=3, b) is 1=2>3, and c) is 1=2=3. What are d) and e)?

immediately after the switch is closed , the inductor behave as open circuit.

for circuit 1 : i = E/(2R)

for circuit 2 : i = E/(3R)

for circuit 3 : i = E/(3R)

hence the order is 1>2=3

After long time , inductor behave as short circuit

for circuit 1 : i = 0

for circuit 2 : i = 0

for circuit 3 : i = 0

so order , 1 = 2 = 3

circuit 1 : i = E/R

circuit 2 : i = E/R

circuit 3 : i = E/R

so order , 1 = 2 = 3

just after the switch is reopened, the Voltage across each inductor is same. so smaller the resistance , greater is the current

so order 3 >1>2

after long time , i = 0

hence 1 = 2 = 3

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