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 a resistor with a higher resistance in this circuit?

Answer 1

Answer:

time constant will decrease and steady state current will decrease on increasing the resistance

Explanation:

As we know that the EMF of cell is E which is used to connected across a resistor and an inductor.

So we will have

$E - iR - L\frac{di}{dt} = 0$

here we know that

$i = \frac{E}{R}(1 - e^{-Rt/L})$

now here we have

$\tau = \frac{L}{R}$

so if we increase the value of resistance of the wire then the time constant will decrease

and hence it will take less time to reach near the steady state value

also the steady state current will be smaller in that case