Episode 127: Capacitors in series and parallel

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

Capacitors in series; capacitors in parallel

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.

Episode 127-1: Capacitors in series and parallel formula derivations (Word, 36 KB)

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.

Episode 127-2: Capacitors in series and parallel questions (Word, 60 KB)

Episode 127-3: More capacitors in series and parallel questions (Word, 28 KB)

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?

Download this episode
Episode 127: Capacitors in series and parallel (Word, 107 KB)