Question

Consider two capacitors with unequal capacitance connected in series 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 potential difference across each capacitor is the same.
3) The charge on each capacitor is the same.
4) The energy stored in each capacitor is the same.

Answer 1

In a series circuit with unequal capacitors, the charge on each capacitor is the same, while the total capacitance, potential difference, and energy stored are not equal to the sum of the individual values.

Step-by-step explanation:

When considering two capacitors with unequal capacitance connected in series to a battery, the following statements are evaluated:

1. The total capacitance of the combination is not equal to the sum of the individual capacitances. Instead, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances.
2. The potential difference across each capacitor is not the same as it depends on their individual capacitances.
3. The charge on each capacitor is the same. This is a consequence of the conservation of charge and the way charges move in a series circuit.
4. The energy stored in each capacitor is not necessarily the same since the energy also depends on the individual capacitances and the voltage across them.

Therefore, in a series circuit, the correct answers are that the charge on each capacitor is the same, and the other statements are false regarding total capacitance, potential difference, and energy stored.