How to increase the energy stored in an inductor by four times?

The correct option is: By doubling the current.

Step-by-step Explanation:

An inductor stores energy within its magnetic field when an electric current flows through it. The formula for the magnetic energy stored in an inductor is given by:

$E=\frac{1}{2}L{I}^2$

where:
• E is the stored energy,
• L is the self-inductance of the inductor, and
• I is the current flowing through the inductor.

From this equation, we can see that the energy stored is directly proportional to the inductance (L) and directly proportional to the square of the current (I²).

Let the initial energy stored be:

$E_1=\frac{1}{2}L{I}_1^2$

We want to find the condition under which the new stored energy (E₂) is four times the initial energy (E₁):

$E_2=4E_1$

If we double the current, the new current becomes:

$I_2=2I_1$

Substituting this new current value into the energy formula (while keeping inductance L constant) gives:

$E_2=\frac{1}{2}L{I}_2^2$

$E_2=\frac{1}{2}L{\left(2I_1\right)}^2$

$E_2=\frac{1}{2}L\cdot 4I_1^2$

We can factor out the constant 4:

$E_2=4\cdot \left(\frac{1}{2}L{I}_1^2\right)$

$E_2=4E_1$

Since the energy is proportional to the square of the current, doubling the current increases the stored energy by a factor of 2² = 4. Thus, the energy is successfully increased by four times by doubling the current.