The switch in the circuit below has been open for a long, long time, R1=8.0 Ohm, R2=5.0 Ohm, L=0.03 H, V=1 V. The internal resistance of the battery is negligibly small.

Determine the currents I1,I2,I3 (in Ampere) in the resistors and in the self-inductor at the moment

(a) just after the switch is closed,

I1:

unanswered

I2:

unanswered

I3:

unanswered
(b) a long time after the switch is closed.

I1:

unanswered

I2:

unanswered

I3:

To determine the currents in the circuit just after the switch is closed, we need to consider the behavior of the circuit elements based on the initial conditions.

(a) Just after the switch is closed:

When the switch is closed, the current starts to flow through the circuit. Initially, the self-inductor (L) acts like a short circuit, allowing the current to flow through it without any opposition. Therefore, the current in the self-inductor (I3) will be maximum initially.

To find the value of current I3, we can use the formula for the initial current in an inductor, which is given by:

I3 (initial) = (V / R2) * (R1 / (R1 + R2))

Here, V is the voltage of the battery, and R1 and R2 are the resistances.

I1 and I2 can be calculated using Ohm's law:

I1 = V / R1
I2 = V / R2

(Alternatively, we can also find I1 and I2 using Kirchhoff's laws. Applying Kirchhoff's loop law to the larger loop containing the resistor R1, battery, and self-inductor L, we can derive the equations I1 = I3 * (R1 / (R1 + R2)) and I2 = I3 * (R2 / (R1 + R2)).)

(b) A long time after the switch is closed:

After a long time, the self-inductor behaves as an open circuit, preventing any current flow through it. This is due to the phenomenon of inductor charging and the establishment of a magnetic field around it.

In this case, the current flowing through the resistors will depend solely on their individual resistances and the available voltage source. Using Ohm's law, we can determine the currents I1 and I2 at this point:

I1 = V / R1
I2 = V / R2

I3 will be zero since the self-inductor acts as an open circuit.

By substituting the given values of resistances and voltage, you should be able to calculate the respective currents in each scenario.