Question

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

Answer 1

Answer:

1. The equivalent capacitance of the combination is greater than the capacitance of either of the capacitors.
2. The voltage across each of the capacitors is the same.
3. The sum of the charge stored on each capacitor is equal to the charge supplied by the battery.

Explanation:

The capacitance connected in parallel will have the same potentials across its ends. If the battery has a charge Q, it is divided among the capacitors.

That is,

                      Q = q₁ + q₂ + q₃

But, the potential is shared equally as V. So, the individual capacitance of the equation has the form q₁ = C₁V , q₂ = C₂V, etc.

                   

So, in this case, when the effective capacitance is formulated, it would be

                          C = C₁ + C₂ + C₃     farad

Therefore, the true statements are

The equivalent capacitance of the combination is greater than the capacitance of either of the capacitors.

The potential across each of the capacitors is the same.

The charge supplied by the battery divided among the capacitors.