Question 230: Electromagnetic Induction

Question

When three inductors of same inductance ' $L$ ' are connected in series and ' I ' is the current passing through the circuit. The energy stored in the circuit is

Accepted Answer

Given:
Three inductors, each of inductance $L$, connected in series.
Current passing through the circuit = $I$
Step 1: Equivalent inductance in series
When inductors are connected in series, their inductances add up:
$$ L_{	ext{eq}} = L_1 + L_2 + L_3 = L + L + L = 3L $$
Step 2: Formula for energy stored in an inductor
The energy stored in an inductor of inductance $L_{	ext{eq}}$ carrying current $I$ is:
$$ E = \frac{1}{2} L_{	ext{eq}} I^2 $$
Step 3: Substitute the values
Substitute $L_{	ext{eq}} = 3L$:
$$ E = \frac{1}{2} 	imes 3L 	imes I^2 = \frac{3}{2} LI^2 $$
Final Answer:
Option
B
$$ \boxed{\frac{3}{2} LI^2} $$

Answer

$\frac{1}{2} \mathrm{LI}^2$

Answer

$\frac{3}{2} \mathrm{LI}^2$

Answer

$\frac{5}{2} \mathrm{LI}^2$

Answer

$\frac{7}{2} \mathrm{LI}^2$

Electromagnetic Induction

When three inductors of same inductance ' L ' are connected in series and ' I ' is the current passing through the circuit. The energy stored in the circuit is

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