Question

Consider two capacitors with unequal capacitance connected in parallel to a battery. Which of the following statements are true?

1) The total capacitance of the combination is equal to the sum of the individual capacitances.
2) The charge on each capacitor is the same.
3) The potential difference across each capacitor is the same.
4) The energy stored in each capacitor is the same.

Answer 1

When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances, the charge on each capacitor is the same, and the potential difference across each capacitor is the same.

Step-by-step explanation:

When capacitors are connected in parallel to a battery, the following statements are true:

1. The total capacitance of the combination is equal to the sum of the individual capacitances. This means that if you have two capacitors with capacitance values C1 and C2, the total capacitance Cp of the combination will be Cp = C1 + C2.
2. The charge on each capacitor is the same. Since the capacitors are connected in parallel, they all have the same voltage across their plates, and therefore the same charge.
3. The potential difference across each capacitor is the same. Again, because the capacitors are connected in parallel and have the same voltage across their plates, the potential difference across each capacitor will be the same.
4. The energy stored in each capacitor is not necessarily the same. The energy stored in a capacitor is given by the formula E = 1/2 * C * V², where C is the capacitance and V is the potential difference across the capacitor. Since the potential difference across each capacitor can be different, the energy stored in each capacitor may also be different.