Circuit laws, series and parallel Cambridge International AS & A Level Physics revision
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In plain words
Two rules sort out any circuit, however tangled. Whatever flows into a junction flows out of it, because charge can't vanish or pile up. And going right round any loop, the energy the batteries give each coulomb equals the energy the components take from it.
4 things to know
- Charge is conserved, so the sum of the currents into a junction equals the sum of the currents out of it. This is known as Kirchhoff's first law.
- Energy is conserved, so round any closed loop the sum of the e.m.f.s equals the sum of the p.d.s. This is known as Kirchhoff's second law.
- In series: the current is the same in each resistor, the p.d.s add up, and R = R₁ + R₂ + ...
- In parallel: the p.d. is the same across each resistor, the currents add up, and 1/R = 1/R₁ + 1/R₂ + ...
Worked example
A 12 V battery of negligible internal resistance is connected to a 4.0 Ω resistor in series with a parallel pair of 6.0 Ω and 3.0 Ω. Find the current from the battery and the p.d. across the parallel pair.
- The parallel pair: 1/R = 1/6.0 + 1/3.0 = 1/2.0, so R = 2.0 Ω.
- Total resistance = 4.0 + 2.0 = 6.0 Ω, so the current = 12 ÷ 6.0 = 2.0 A.
- P.d. across the pair = 2.0 × 2.0 = 4.0 V. (The other 8.0 V is across the 4.0 Ω.)
Tips and tricks
- The combined resistance of resistors in parallel is always less than the smallest of them.
- Simplify a circuit one step at a time: replace each parallel group with a single resistor, then add up the series ones.
It lands in your notebook with its questions as flashcards.
Circuit laws, series and parallel: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
Why does the total current flowing into a junction equal the total current flowing out?
Charge can't be created, destroyed or stored at a junction.
What is the combined resistance of two 10 Ω resistors in parallel?
1/R = 1/10 + 1/10.
What is the combined resistance of three 6 Ω resistors in series?
In series, resistances add.
Round any closed loop, the e.m.f.s add up to the same as the p.d.s. Which principle does that follow from?
The energy given to each coulomb equals the energy taken from it.
Two resistors are connected in parallel. What is the same for both?
They are connected between the same two points.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 9 marks. Write your answers on paper, then check them.
Circuit laws, series and parallel
Cambridge International AS & A Level Physics 9702 · 9 marks · papermunch.org
Name ______________________________ Date ______________
Find the combined resistance of 6.0 Ω and 3.0 Ω in parallel.[2]
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2.0 Ω.
The rule for currents at a junction and the rule for p.d.s round a loop each follow from a conservation law. State which.[2]
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The rule for currents at a junction follows from the conservation of charge. The rule for p.d.s round a loop follows from the conservation of energy.
Currents of 2.0 A and 3.0 A flow into a junction, and 1.5 A flows out along one wire. Find the current in the only other wire, and its direction.[2]
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3.5 A, out of the junction.
Use the conservation of charge and of energy to show that two resistors in series have a combined resistance R = R₁ + R₂.[3]
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The current I is the same in both, because charge is conserved. The p.d. across the pair is V = V₁ + V₂, because energy is conserved. So IR = IR₁ + IR₂, and dividing by I gives R = R₁ + R₂.
Answers: Circuit laws, series and parallel
- 1. 2.0 Ω.
- 2. The rule for currents at a junction follows from the conservation of charge. The rule for p.d.s round a loop follows from the conservation of energy.
- 3. 3.5 A, out of the junction.
- 4. The current I is the same in both, because charge is conserved. The p.d. across the pair is V = V₁ + V₂, because energy is conserved. So IR = IR₁ + IR₂, and dividing by I gives R = R₁ + R₂.