An inductor having self inductance L with its coil resistance R is connected accrodd a battery of emf E. When circuit is in steady state at t=0 an iron rod is inserted into the inductor due to which its inductance becomes nL(n>1).

Q1.After insertion of rod which of the following quantities will change with time?

1.Potential difference

2.inductance

3.Rate of heat production in coil

(a) only 1 (b) 1 and 3 (c)only 3 (d) 1,2 and 3

Q2.After insertion of rod,current in the circuit:

a)Increases with time

b)Decreases with time

c)Remains constant with time

d)First decreases with time then becomes constant

Let's break down the scenario you've presented regarding the inductor, its self-inductance, and the effects of inserting an iron rod into the coil. This involves understanding how inductance, potential difference, and heat production in the coil interact in an electrical circuit.

Understanding the Circuit Dynamics

Initially, when the circuit is connected to a battery with an electromotive force (emf) E, the inductor has a self-inductance L and a resistance R. In a steady state (at t=0), the current through the inductor reaches a constant value, and the potential difference across the inductor is zero because the inductor behaves like a short circuit at steady state.

Effects of Inserting the Iron Rod

When you insert an iron rod into the inductor, the inductance increases to nL (where n > 1). This change in inductance affects several quantities in the circuit:

• Potential Difference: The potential difference across the inductor will change because the inductance has increased. According to the formula for inductance, V = L (di/dt), if L increases, the potential difference must adjust to maintain the relationship with the changing current.
• Inductance: Clearly, the inductance itself changes from L to nL. This is a direct consequence of inserting the iron rod, which increases the magnetic permeability and thus the inductance.
• Rate of Heat Production: The rate of heat production in the coil, given by P = I²R, will also change. As the inductance increases, the current will adjust over time, affecting the power dissipated as heat.

Answering the Questions

Now, let's address your questions directly:

Q1: After insertion of the rod, which of the following quantities will change with time?

The correct answer is (d) 1, 2, and 3. All three quantities will change due to the insertion of the rod:

• The potential difference will change as the inductance increases.
• The inductance itself changes from L to nL.
• The rate of heat production will vary as the current adjusts in response to the increased inductance.

Q2: After insertion of the rod, the current in the circuit:

The correct answer is (d) First decreases with time then becomes constant. Initially, the current will decrease because the increased inductance opposes the change in current (according to Lenz's law). Over time, as the circuit stabilizes, the current will reach a new steady state value.

Conclusion

In summary, inserting an iron rod into the inductor changes the inductance and affects the potential difference and heat production in the coil. The current will initially decrease before stabilizing at a new constant value. This behavior illustrates the dynamic nature of inductive circuits and the principles of electromagnetism at play.