State Kirchhoff's second law.

Around a closed loop, the sum of the e.m.f.s equals the sum of the potential differences.

What is the same for components in series?

The current, because charge cannot accumulate.

What is the same for components in parallel?

The potential difference, as they are connected across the same two points.

Why is the parallel combination always smaller than the smallest resistor?

Each extra branch gives charge another route, so more current flows for the same p.d.

Derive R = R₁ + R₂ in one line.

Same I, V = V₁ + V₂, so IR = IR₁ + IR₂, giving R = R₁ + R₂.

Derive 1/R = 1/R₁ + 1/R₂ in one line.

I = I₁ + I₂ with the same V, so V/R = V/R₁ + V/R₂, giving 1/R = 1/R₁ + 1/R₂.

What happens to the total resistance when a parallel branch is removed?

It increases, so the total current falls.

Kirchhoff's laws and combining resistorsEdexcel International A Level Physics: Flashcards

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State Kirchhoff's first law.

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State Kirchhoff's first law.: The sum of the currents entering a junction equals the sum of the currents leaving it.
Which conservation law underlies Kirchhoff's first law?: Conservation of charge.
State Kirchhoff's second law.: Around a closed loop, the sum of the e.m.f.s equals the sum of the potential differences.
Which conservation law underlies Kirchhoff's second law?: Conservation of energy.
What is the same for components in series?: The current, because charge cannot accumulate.
What is the same for components in parallel?: The potential difference, as they are connected across the same two points.
Give the equation for resistors in series.: R = R₁ + R₂ + ...
Give the equation for resistors in parallel.: 1/R = 1/R₁ + 1/R₂ + ...
Why is the parallel combination always smaller than the smallest resistor?: Each extra branch gives charge another route, so more current flows for the same p.d.
Derive R = R₁ + R₂ in one line.: Same I, V = V₁ + V₂, so IR = IR₁ + IR₂, giving R = R₁ + R₂.
Derive 1/R = 1/R₁ + 1/R₂ in one line.: I = I₁ + I₂ with the same V, so V/R = V/R₁ + V/R₂, giving 1/R = 1/R₁ + 1/R₂.
What happens to the total resistance when a parallel branch is removed?: It increases, so the total current falls.

Exam questions on Kirchhoff's laws and combining resistors

A technician connects a 12 V battery of negligible internal resistance in series with a 4.0 Ω resistor and an 8.0 Ω resistor.
Calculate the potential difference across each resistor and show that your values are consistent with conservation of energy.2 marks
A 6.0 Ω resistor and a 3.0 Ω resistor are connected in parallel across a 9.0 V battery of negligible internal resistance.
Calculate the current in each resistor and show that the total current is consistent with conservation of charge.2 marks
A teacher wants to show that the equations for combining resistors can be derived from conservation laws. She considers two resistors, R₁ and R₂, connected to a supply of potential difference V. First they are connected in series, with total current I, and then in parallel, with total current I.
Use conservation laws to derive the equation for the total resistance R of two resistors in series.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).