Question

Part A (1.5 pts) Circle the letter of the phrase that most accurately completes the sentence.

When the current in the circuit below increases from 0.50 Io to Io the emf induced in the inductor acts in the:

1. the same direction as ?? and the energy stored in the inductor is 2x the initial value

2. the opposite direction to ?? and the energy stored in the inductor is 2x the initial value.

3. the same direction as ?? and the energy stored in the inductor is 4x the initial value.

4. the opposite direction to ?? and the energy stored in the inductor is 4x the initial value.

Answer 1

Part A : Circle the letter of the phrase that most accurately completes the sentence.

When the current in the circuit below increases from 0.50 Io to Io the emf induced in the inductor acts in the :

• the opposite direction to ?? and the energy stored in the inductor is 2x the initial value.

Option (ii) : it will be correct.

Explanation : Suppose that an inductor of inductance (L) is connected to a variable DC voltage supply.

The supply is adjusted so as to increase the current (i) flowing through an inductor from zero to some final value (I).

As the current through an inductor is ramped up, an emf is generated which acts to oppose the increase in a current.

Work done by the voltage source during a time interval is given by -

dW = P dt = - i dt

dW = i L (di / dt) dt

dW = L i di

To find the total work done in establishing the final current (I) in an inductor, we must integrate an above expression.

Then, we have

W = L i di

W = (1/2) L I²

From work-energy theorem, we have

E = W = (1/2) L I₀²

The energy stored in an inductor which will be given as -

E = (1/2) L [I₀ - (0.5) I₀]²

E = (1/2) L [(0.5) I₀]²

E = (0.25) [(1/2) L I₀²]