A capacitor is charged with a battery and energy stored is U. after disconnecting the battery another capacitor of same capacity is connected in parallel with it. The energy stored in each capacitor is.
To calculate the energy stored in each capacitor after connecting them in parallel, we need to understand how capacitors store energy and how they behave when connected in parallel.
1. Energy stored in a capacitor: The energy stored in a capacitor can be calculated using the formula U = (1/2) * C * V^2, where U is the energy stored, C is the capacitance, and V is the voltage across the capacitor.
2. Capacitors in parallel: When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances. In this case, since the two capacitors have the same capacity (C), the total capacitance (C_total) will be double the individual capacitance, i.e., C_total = 2C.
Now, let's calculate the energy stored in each capacitor after connecting them in parallel.
Step 1: Given that the energy stored in the initial capacitor is U.
Step 2: Since the capacitors have the same capacitance, the total capacitance after connecting them in parallel is C_total = 2C.
Step 3: When capacitors are connected in parallel, the voltage across each capacitor is the same. So, the voltage across each capacitor will be the same as the initial voltage.
Step 4: Substitute the values in the energy formula U = (1/2) * C_total * V^2,
U = (1/2) * (2C) * V^2
U = 2CV^2
Hence, after connecting the capacitors in parallel, the energy stored in each capacitor will be 2CV^2, where C is the individual capacitance and V is the voltage across each capacitor.