# A 3.1-µF capacitor has a voltage of 31 V between its plates. What must be the current in a 5.6-mH inductor so that the energy stored in the inductor equals the energy stored in the capacitor?

## (1/2) L i^2 = (1/2) C V^2

i^2 = (C/L) V^2

i^2 = (3.1*10^-6 / 5.6*10^-3) (961)

i^2 = 532 * 10^-3 = 53.2 * 10^-4

i = 7.3 * 10^-2 = .073 amps

## To find the current in the inductor, we need to equate the energy stored in the capacitor to the energy stored in the inductor.

The energy stored in a capacitor can be calculated using the formula:

E_capacitor = (1/2) * C * V^2

where C is the capacitance and V is the voltage across the capacitor.

The energy stored in an inductor can be calculated using the formula:

E_inductor = (1/2) * L * I^2

where L is the inductance and I is the current through the inductor.

We can equate these two energies to find the current in the inductor:

(1/2) * C * V^2 = (1/2) * L * I^2

Rearranging the equation, we have:

I^2 = (C * V^2) / L

Taking the square root of both sides, we get:

I = sqrt((C * V^2) / L)

Now we can substitute the given values:

C = 3.1 µF = 3.1 * 10^-6 F
V = 31 V
L = 5.6 mH = 5.6 * 10^-3 H

Plugging in these values into the equation:

I = sqrt((3.1 * 10^-6 * 31^2) / (5.6 * 10^-3))

Calculating this expression, we find:

I ≈ 0.803 A

Therefore, the current in the 5.6 mH inductor must be approximately 0.803 A in order for the energy stored in the inductor to equal the energy stored in the capacitor.

## To find the current in the inductor, we need to equate the energy stored in the capacitor with the energy stored in the inductor.

Let's start by calculating the energy stored in the capacitor. The energy stored in a capacitor can be found using the formula:

E = (1/2) * C * V^2

where E is the energy stored in the capacitor, C is the capacitance, and V is the voltage across the plates of the capacitor.

Plugging in the given values, we have:

E_capacitor = (1/2) * 3.1 * 10^-6 F * (31 V)^2

Now, let's calculate the energy stored in the inductor. The energy stored in an inductor is given by the formula:

E = (1/2) * L * I^2

where E is the energy stored in the inductor, L is the inductance, and I is the current flowing through the inductor.

We want the energy stored in the inductor to be equal to the energy stored in the capacitor, so we can equate the two:

(1/2) * L * I^2 = (1/2) * C * V^2

Now we can solve for the current (I):

I^2 = (C * V^2) / L

I = sqrt( (C * V^2) / L )

Plugging in the given values, we can now calculate the current.

I = sqrt( (3.1 * 10^-6 F * (31 V)^2) / (5.6 * 10^-3 H) )

I ≈ 0.218 A (rounded to three decimal places)

Therefore, the current in the 5.6-mH inductor should be approximately 0.218 Amps in order for the energy stored in the inductor to equal the energy stored in the capacitor.