The derivation of formulae for capacitors in series and parallel will help to reinforce your students’ understanding of circuits involving capacitors.

Summary

Discussion: Deriving the formulae. (20 minutes)

Worked examples: Using the formulae. (10 minutes)

Student questions: Using the formulae. (30 minutes)

Student experiment: Checking the formulae. (20 minutes)

Discussion:

Deriving the formulae

Your students will have encountered the idea of replacing resistors in series and parallel by a single resistor which has the same effect in the circuit. Remind them of this as an introduction but be ready to dispel any confusion that may arise because the formulae are ‘reversed’ for capacitors.

For capacitors in parallel the pd across each is the same. For capacitors in series, it is the charge stored that is the same.

TAP 127-1: Capacitors in series and parallel formula derivations

Worked examples:

Using the formulae

Choose a couple of simple examples; say, 20 mF and 30 mF in parallel (= 50 mF), and then in series (= 12 mF). Point out that capacitors in parallel combine to give a greater capacitance; in series, the resultant is less than either. What about equal capacitors? (In series, half the capacitance of either.)

Student questions:

Using the formulae

Questions 1 and 2 can reinforce the above discussion. Questions 3 and 4 give practice in using the formulae.

TAP 127-2: Capacitors in series and parallel questions

TAP 127-3: More capacitors in series and parallel questions

Student experiment:

Checking the formulae

If a capacitance meter is available, the results of some of the calculations above can be checked experimentally and/or further combinations can be tried. Provide students with two (or more) capacitors whose values they can measure. They can then connect them together, first in parallel and then in series. Does the meter reading agree with calculated values?

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