# Rank the circuits based on the current through the battery immediately after the switch is closed.?

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Rank the circuits based on the current through the battery immediately after the switch is closed.

Rank from largest to smallest. To rank items as equivalent, overlap them

My Analysis, based on text book, the inductors can be considered to be not having any resistance.

A – 2 Resistors in series

B – 2 Resistors in series

C – 1 resistor

D – 1 resistor in parallel with inductor

E – 2 resistors in parallel with inductor

F – 2 resistors in parallel with inductor

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Therefore : E=F > D > C > A=B

• Immediately after the switch is closed, the inductor acts as an open circuit. So

E >A =D>F>B =C

Since E has two resistors and an inductor in parallel, it will have the highest current I= V/(½R) = 2V/R  due to two resistors in parallel

After the switch is closed circuits A and D act as a resistor in parallel with a battery (I =V/R) since the inductors in each circuit as an open.

Circuit F  acts as 2 resistors in series when the switch is closed (I =V/(2R)

Circuits B and C don’t draw any initial current as the inductor in each circuit initially acts as an open

• iL(t) = V/R *(1-e^-R*t/L) so we know that immediately after the switch is closed, iL = 0 as if it is not in the circuit.

E, A = D, F,C,B 