# A coil with 10 Ω resistance and 2 H inductance is connected to a 50 V battery. What will be the energy stored in the coil?

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A coil with 10 Ω resistance and 2 H inductance is connected to a 50 V battery. What will be the energy stored in the coil?
1. 25 J
2. 50 J
3. 75 J
4. 100 J

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Correct Answer - Option 1 : 25 J

Concept:

The power stored in an inductor is given by

⇒ P = Vi      -----(1)

Where V = Voltage induced in an inductor, and i = current

The voltage induced in the inductor is given by

$⇒V =L\frac{dI}{dt}$

Substituting the above equation in equation 1, it becomes

$⇒P = L i \frac{dI}{dt}$

The energy stored in the inductor is given by

$⇒E = \int P dt$

Substituting the value of P in the above equation

$⇒ E = \int L i\frac{dI}{dt}dt$

$⇒ E = \int L i di$

$⇒ E = \frac{1}{2} LI^{2}$

Calculation:

R = 10 Ω, L = 2 H

I = 50 / 10 = 5 A

E = ( 2 × 52 )  / 2

= 25 J