Next: Example 6.4: Energy stored Up: Capacitance Previous: Example 6.2: Dielectric filled

## Example 6.3: Equivalent capacitance

Question: A and a capacitor are connected in parallel, and this pair of capacitors is then connected in series with a capacitor, as shown in the diagram. What is the equivalent capacitance of the whole combination? What is the charge on the capacitor if the whole combination is connected across the terminals of a V battery? Likewise, what are the charges on the and capacitors?

Answer: The equivalent capacitance of the and capacitors connected in parallel is . When a capacitor is combined in series with a capacitor, the equivalent capacitance of the whole combination is given by

and so

The charge delivered by the V battery is

This is the charge on the capacitor, since one of the terminals of the battery is connected directly to one of the plates of this capacitor.

The voltage drop across the capacitor is

Thus, the voltage drop across the and combination must be . The charge stored on the is given by

Likewise, the charge stored on the capacitor is

Note that the total charge stored on the and combination is , which is the same as the charge stored on the capacitor. This makes sense because the and combination and the capacitor are connected in series.

Next: Example 6.4: Energy stored Up: Capacitance Previous: Example 6.2: Dielectric filled
Richard Fitzpatrick 2007-07-14