1. The figure below shows three circuits with identical batteries, inductors, an

Question

1. The figure below shows three circuits with identical batteries, inductors, and resistors. The emf of each battery is E, the resistance of each resistor is R, and the inductance of each inductor is L. Unless stated otherwise, put all answers in terms of E, R, L, and physical constants.

a. For each of the three circuits shown above, determine the current through the battery immediately after the switch is closed.

b. For each of the three circuits shown above, determine the current through the battery a long time after the switch is closed.

c. For each of the three circuits shown above, determine the magnetic potential energy stored in the magnetic field of the inductor a long time after the switch is closed.

The figure below shows three circuits with identical batteries, inductors, and resistors. The emf of each battery is E, the resistance of each resistor is R, and the inductance of each inductor is L. Unless stated otherwise, put all answers in terms of E, R, L, and physical constants. For each of the three circuits shown above, determine the current through the battery immediately after the switch is closed. For each of the three circuits shown above, determine the current through the battery a long time after the switch is closed. For each of the three circuits shown above, determine the magnetic potential energy stored in the magnetic field of the inductor a long time after the switch is closed.

Explanation / Answer

Property of an inductor::

1) Inductor behaves as insulator just after the connection(open circuit)

2) inductor behaves as conductor a long time after connection(short circuit)

a) at t=0

I1= 0

I2=E/R

I3= E/2R

b) at t= infinity

I1=E/2R

I2=2E/R

I3=E/R

c)

now firse we have to calculate the currect through the inductor

I1= E/2R

I2= E/R

I3 = E/R

so energy = 0.5LI^2

==> Energy 1 = (1/2) *L*(E/2R)^2=(1/8)*(LE^2/R^2)

==> Energy 2 = (1/2) *L*(E/R)^2=(1/2)*(LE^2/R^2)

==> Energy 3 = (1/2) *L*(E/R)^2=(1/2)*(LE^2/R^2)

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