A capacitor is connected with a battery and stores energy U.
After removing the battery,its connected with another similar capacitor in parallel. What will be the new stored energy in each capacitor?
is ne body there to help me actully it's very urgent
i know that its answer is U/4
but i don't know the method right now.
To find the new stored energy in each capacitor, we need to consider the fact that capacitors in parallel share the voltage across them and each capacitor acquires charge as per its capacitance. Let's assume the original capacitor has capacitance C1 and stores energy U.
When the original capacitor is connected with a battery, it charges up and stores energy U. Now, when we remove the battery and connect it with another similar capacitor (let's call it C2) in parallel, the combination of capacitors will act as a single equivalent capacitor (let's call it Ce).
In parallel connection, the total capacitance is the sum of the individual capacitances. Therefore, the equivalent capacitance Ce will be:
Ce = C1 + C2
Since the capacitors are connected in parallel, the voltage across each capacitor is the same as the voltage across the combination (assuming negligible internal resistance of the capacitors).
Now, the stored energy in a capacitor is given by the formula:
U = 0.5 * C * V^2
Where U is the stored energy, C is the capacitance, and V is the voltage across the capacitor.
Since the voltages across both capacitors are the same (equal to the voltage across the combination), the energy stored in each capacitor, U1 and U2 respectively, will be:
U1 = 0.5 * C1 * V^2
U2 = 0.5 * C2 * V^2
Substituting the value of V^2 (which remains constant) into the equations:
U1 = 0.5 * C1 * (V^2)
U2 = 0.5 * C2 * (V^2)
As we are connecting capacitors in parallel, the voltage across the combination (and each capacitor) remains the same. Therefore, the stored energy in each capacitor will be directly proportional to their individual capacitances.
Hence, the new stored energy in each capacitor will be U1 = 0.5 * C1 * (V^2) and U2 = 0.5 * C2 * (V^2), where C1 is the capacitance of the original capacitor and C2 is the capacitance of the additional capacitor.