After a parallel-plate capacitor is charged by a battery, it is disconnected from the battery and its plate separation is increased. Which of the following statements is correct?
There are no following statements.
Cutting and pasting questions often does not work here. It would be much better if you would type in your questions and show some effort of your own towards solution.
To determine which of the following statements is correct in this scenario, we must understand the behavior of a parallel-plate capacitor when it is charged by a battery and then disconnected from the battery with an increased plate separation. Let's analyze each statement:
1. The potential difference across the capacitor decreases.
2. The energy stored in the capacitor increases.
3. The capacitance of the capacitor decreases.
To determine if these statements are correct, we need to consider the fundamental properties of a capacitor.
1. Potential Difference: The potential difference across a charged capacitor is given by V = Q/C, where V is the potential difference, Q is the charge on the capacitor, and C is the capacitance. If we increase the plate separation, the charge on the capacitor remains constant because it is disconnected from the battery. Therefore, the potential difference across the capacitor would increase, not decrease. So, Statement 1 is incorrect.
2. Energy Stored: The energy stored in a capacitor is given by U = 0.5 * C * V^2, where U is the energy, C is the capacitance, and V is the potential difference. If the plate separation is increased while the capacitor is disconnected from the battery, only the potential difference changes. Since the potential difference increases (as explained in Statement 1), the energy stored in the capacitor would increase. Hence, Statement 2 is correct.
3. Capacitance: The capacitance of a parallel-plate capacitor is given by C = (ε₀ * A) / d, where C is the capacitance, ε₀ is the permittivity of free space, A is the area of the plates, and d is the plate separation. If the plate separation is increased, the capacitance would decrease, according to the formula. Therefore, Statement 3 is correct.
In conclusion, Statements 2 and 3 are correct, while Statement 1 is incorrect.