- Energy Stored in a Capacitor Definition: A capacitor stores energy by holding an electric charge on its plates.
- Charging Process: When connected to a battery, charges move to the capacitor plates, increasing its voltage and stored energy.
- Work Done to Store Charges: Subsequent charges need work to overcome repulsion from existing charges on the plates.
- Voltage Changes During Charging: The capacitor’s voltage changes until it equals the battery’s voltage.
- Energy Loss During Charging: Half of the energy from the battery is stored in the capacitor, and the other half is lost.
When a capacitor is connected to a battery, charges move from the battery to the capacitor plates step by step.
At the very beginning, capacitor does not have any charge or potential. i.e. V = 0 volts and q = 0 C.
When first connected, the full battery voltage is applied across the capacitor. The first charge moves to the positive plate without any work since the capacitor initially has no voltage of its own. This first charge creates a small voltage, making it harder for the second charge, which gets repelled by the first. As the battery voltage is higher, the second charge still moves to the positive plate.
At that condition a little amount of work is to be done to store second charge in the capacitor. Again for the third charge, same phenomenon will appear. Gradually charges will come to be stored in the capacitor against pre-stored charges and their little amount of work done grows up.
The capacitor voltage is not fixed; it starts at zero and increases until it matches the battery voltage.
As more charges are stored, the capacitor’s voltage and energy increase.
So at that point of discussion the energy equation for the capacitor can’t be written as energy (E) = V.q
As the voltage increases the electric field (E) inside the capacitor dielectric increases gradually but in opposite direction i.e. from positive plate to negative plate.
Here dx is the distance between two plates of the capacitor.
Charge will flow from battery to the capacitor plate until the capacitor gains as same potency as the battery.
So, we have to calculate the energy of the capacitor from the very begging to the last moment of charge getting full.
Suppose, a small charge q is stored in the positive plate of the capacitor with respect to the battery voltage V and a small work done is dW.
Then considering the total charging time, we can write that,
Now we go for the energy loss during the charging time of a capacitor by a battery.
As the battery is in the fixed voltage the energy loss by the battery always follows the equation, W = V.q, this equation is not applicable for the capacitor as it does not have the fixed voltage from the very beginning of charging by the battery.
Now, the charge collected by the capacitor from the battery is
Now charge lost by the battery is
Half of the energy from the battery is stored in the capacitor, while the other half is lost.
