Question

A 12.0 V dc battery having no appreciable internal resistance, a 150.5 ohm resistor, an 11.2 mH inductor, and an open switch are all connected in series.
A)After the switch is closed, what is the time constant for this circuit ? 74.4 micro seconds
B)After the switch is closed, what is the maximum current that flows through it ? in A
C) What is the current 73.4 micro seconds after the switch is closed ? in A
D)After the switch is closed, what is the maximum energy stored in the inductor? in micro J

Answer 1

Concepts and reason

The concepts used to solve this problem are time constant, ohm’s law, current in RL circuit, and energy stored in inductor.

First, use the inductance and resistance to determine the time constant of the circuit.

Then, use the Ohm’s law to determine the maximum current in the circuit.

Use the relation between time constant and maximum current to determine the current at the given time.

Finally, use the relation between inductance and maximum current in the circuit to determine the energy stored in it.

Fundamentals

The time constant is the required time by a circuit which allows the current to attain of its maximum value.

The expression for time constant in an RL circuit is given below:

Here, the time constant is , the inductance is , and the resistance is .

According to Ohm’s law, the potential difference between the two pints of a wire is directly proportional to the current passing through the wire. The constant of proportionality is called the resistance.

The expression for Ohm’s law is given below:

Here, the maximum current is , the voltage is , and the resistance is .

The expression for current in the circuit at time is given below:

Here, the current in the circuit is , the resistance is , the time is , and the inductance is .

The expression for energy stored in the inductor is given below:

Here, the energy stored in the inductor is , and the inductance is .

(A)

The expression for the time constant of the RL circuit is given below:

Substitute for , and for .

(B)

The expression for maximum current is given below:

Substitute for , and for .

(C)

The expression for current in the RL circuit is given below:

Replace with in the above expression.

Substitute for , and for , and for .

(D)

The expression for energy stored in the inductor is given below:

Substitute for , and for .

Ans: Part A

The time constant of the circuit is .

Part B

The maximum current in the circuit is .

Part C

The current through the circuit after is .

Part D

The energy stored in the inductor is .