Question

The energy stored in a coil carrying current I is U. If current is halved, the energy stored in the coil will be

Answer 1

Answer:

1. answer is 1/4

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Answer 2

Given : Energy stored in a coil carrying current I is U.

To Find : Energy stored in the coil, if current is halved.

Solution :

Energy stored in a coil carrying current I is U

Then,

$\[U = \frac{1}{2}L{I^2}\]$

According to expression ,

$\[U \propto {I^2}\]$

Thus

$\[\frac{U}{{{U_2}}} = {\left( {\frac{I}{{{I_2}}}} \right)^2}\]$

where,

U = Energy stored in the coil when the current is I.

$\[{{U_2}}\]$ = Energy stored in the coil when current is halved.

I = Current when energy stored in coil is U

$\[{{I_2}}\]$ = $\[\frac{I}{2}\]$   As current is halved

Now putting in above equation

$\[\frac{U}{{{U_2}}} = {\left( {\frac{I}{{{I_2}}}} \right)^2}\]$

$\[\frac{U}{{{U_2}}} = {\left( {\frac{I}{{I/2}}} \right)^2}\]$

$\[{U_2} = \frac{U}{4}\]$

Hence the energy stored in coil when current is halved is U/4