Question

Starting from zero, an electric current is established in a circuit made of a battery of emf E, a resistor of resistance R and an inductor of inductance L. The electric current eventually reaches its steady-state value. What would be the effect of using an inductor with a larger inductance in this circuit?

A)
The steady-state value of the current would be larger, but it would take the same amount of time to reach it.
B)
The steady-state value of the current would be the same, but it would take more time to reach it.
C)
The steady-state value of the current would be the same, but it would take the same amount of time to reach it.
D)
The steady-state value of the current would be larger, but it would take more time to reach it.
E)
The steady-state value of the current would be the same, but it would take less time to reach it.

What�s the answer? I need justification as well.

Answer 1

Answer: D)

Step-by-step explanation:

In a RL circuit, as current can't change instantaneously, it starts from 0, till it reaches to the maximum possible value, according to Ohm's Law, i.e., E/R.

At any time, the current in the circuit (which is the same that passes through the inductor as it's a series circuit) is explained by the following equation:

I = E/R (1 - e-tR/L)

The quotient L/R is called the time constant of the circuit, and defines the time needed for the current reaches to its steady-state value.

If L is larger, the time constant will be larger, and it will take more time to the current to reach to its steady-state value.