Show that in a parallel plate capacitor the stored electric energy is Ue=C(V^2)/2 where C is the capacity and V the voltage. (Hint: Remember that in a capacitor Q=CV)

Question

Show that in a parallel plate capacitor the stored electric energy is Ue=C(V^2)/2 where C is the capacity and V the voltage. (Hint: Remember that in a capacitor Q=CV)

Thanks.

Answer 1

Your first step, is that you consider the electric field across the plates of the capacitor. When you take any small charge = dq from one plate of the capacitor to another, work will be done due to the presence of this electric field. That work is essentially the energy that the capacitor stores.

For a small charge dq, the work done in this process = dW = V*dq

Because we know that work is equal to the charge multiplied by the potential difference

Now, plug in V = Q/C, which is the standard equation for a capacitor.

You get dW = (1/C)*(Q*dq)

Integrate both sides, and you'll get your term for energy stored in a capacitor.

Answer 2

or say power = V i = V dQ/dt

but
Q = V C
so
V i = (1/C) Q dQ/dt (same as Arora did)
energy = power *time = (1/C) Q^2/2 = C V^2/2

Answer 3

To show that the stored electric energy in a parallel plate capacitor is given by Ue = C * (V^2) / 2, we can start with the equation for the energy stored in a capacitor.

The energy stored in a capacitor is given by the equation:

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

where Ue is the stored energy, C is the capacitance, and V is the voltage across the capacitor.

To prove this equation, we can use the relationship between voltage, charge, and capacitance.

The charge stored in a capacitor is given by the equation:

Q = C * V

where Q is the charge stored, C is the capacitance, and V is the voltage.

Now, we can substitute the expression for charge (Q) into the equation for energy (Ue) to get:

Ue = (1/2) * (Q / C) * V

Since Q = C * V, we can substitute this into the equation:

Ue = (1/2) * [(C * V) / C] * V

Simplifying this expression gives:

Ue = (1/2) * V^2

This proves that the stored electric energy in a parallel plate capacitor is given by Ue = C * (V^2) / 2.

To summarize:
1. Start with the equation for stored energy in a capacitor: Ue = (1/2) * C * (V^2).
2. Use the relationship between charge, voltage, and capacitance: Q = C * V.
3. Substitute the expression for charge (Q) into the equation for energy (Ue).
4. Simplify the equation to get Ue = (1/2) * V^2, which proves the desired equation.

Show that in a parallel plate capacitor the stored electric energy is Ue=C*(V^2)/2 where C is the capacity and V the voltage. (Hint: Remember that in a capacitor Q=C*V)

Your first step, is that you consider the electric field across the plates of the capacitor. When you take any small charge = dq from one plate of the capacitor to another, work will be done due to the presence of this electric field. That work is essentially the energy that the capacitor stores.

or say power = V i = V dQ/dt

To show that the stored electric energy in a parallel plate capacitor is given by Ue = C * (V^2) / 2, we can start with the equation for the energy stored in a capacitor.

Show that in a parallel plate capacitor the stored electric energy is Ue=C(V^2)/2 where C is the capacity and V the voltage. (Hint: Remember that in a capacitor Q=CV)