Capacitors in Series and Parallel

Capacitors connected across the same two nodes have the same potential difference. Each stores charge proportional to its own capacitance. The supply provides the sum of these charges, so replacing the combination by one capacitor gives the sum rule.

Identify nodes from electrical connections, not from how close components are drawn on the page. Adding another parallel capacitor increases the total charge that can be stored at the same voltage. The largest individual capacitance must therefore be smaller than the total.

In an initially uncharged series chain with isolated intermediate junctions, equal and opposite charges are induced on neighbouring plates. Each capacitor therefore has the same charge magnitude Q. Their potential differences Q/C add to the supply voltage, giving the reciprocal rule.

The smaller capacitor has the larger voltage because V=Q/C. The equivalent series capacitance is smaller than the smallest component. A component’s voltage rating must be checked against its own voltage, not assumed to be half the supply unless capacitances are equal.

Use a suitable low-voltage source, known capacitor values, meters and a controlled charge/discharge circuit. Compare individual and combined charge or discharge time constants through the same known resistor, allowing for the meter input resistance. The ratio of time constants gives the ratio of effective capacitances when effective resistance is unchanged.

Observe capacitor polarity and voltage ratings and discharge through an appropriate resistor before reconnecting. Compare results with component tolerances rather than expecting the printed nominal values to match exactly. Check for leakage if a combination loses charge unexpectedly quickly.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.