Electrical circuits | OCR A Level Physics revision

OCR A H556 · Module 4 · Section 4.3

Electrical circuits

Analyse unfamiliar networks with conservation laws, then investigate real cells and design potential-divider sensors. Every model asks you to predict the direction of change before calculating.

14 specification pointsThree circuit modelsTwo practical investigations
Exam-style diagrams of a cell with internal resistance, a potential divider and a terminal-potential-difference graph
A real source has internal resistance; a potential-divider output depends on the component between the output point and 0 V.

Redraw, conserve, check

1

Redraw

Mark junctions and trace which components share the same two nodes.

2

Conserve

Use charge at junctions and energy around complete loops.

3

Check

Parallel resistance must be below the smallest branch resistance; a divider output must lie between 0 and Vin.

Kirchhoff’s laws and resistor networks

First law: junctions

ΣI in = ΣI out

This follows from conservation of charge.

Second law: loops

Σε = ΣV

Around a complete loop, energy supplied per charge equals energy transferred per charge.

Series resistance

R = R₁ + R₂ + …

The same current flows through each series component.

Parallel resistance

1/R = 1/R₁ + 1/R₂ + …

Each branch has the same p.d.

Several sources

Choose a loop direction. Sources traversed from negative to positive add e.m.f.; opposing sources subtract.

Unfamiliar layout?Do not decide “series” or “parallel” by appearance. Components are parallel only when both ends connect to the same pair of nodes.

Series and parallel circuit laboratory

Predict the total resistance first

Switch the same resistors between series and parallel. Check whether your calculated total passes the physical sense check.

E.m.f., terminal p.d. and internal resistance

ε = I(R + r)

The current is limited by the external load resistance R and the internal resistance r of the source.

ε = V + Ir

Terminal p.d. V is the energy per charge delivered to the external circuit. Ir is the “lost volts” inside the source.

Physical checkWhen a source supplies current, terminal p.d. is normally below its e.m.f. It approaches e.m.f. when current approaches zero.

Real-cell investigation

Predict how lowering the load resistance affects current, lost volts and terminal p.d. Then move one control.

Determining internal resistance experimentally

  1. Connect the cell, switch, ammeter and variable resistor in series; connect a voltmeter across the cell.
  2. Change the current and record paired terminal-p.d. and current readings. Open the switch between readings to reduce changes in cell temperature.
  3. Plot V against I. From V = ε − Ir, the vertical intercept is ε and the gradient is −r.
Graph languageIf asked for internal resistance from the gradient, report the positive magnitude of the negative gradient and include Ω.

Potential dividers and sensor circuits

Vout = Vin × Rbottom / (Rtop + Rbottom)

The numerator is the resistance across which Vout is measured. A potentiometer provides a continuously variable output by moving the contact along a resistive track.

Sensor-divider designer

Choose whether the sensor is above or below the output. Predict the complete chain: stimulus → sensor resistance → output p.d.

Full-mark explanation patternState how the stimulus changes sensor resistance, identify whether that resistance is above or below Vout, then state and justify the direction in which Vout changes.

Analyse and justify

Q1. Resistors of 6.0 Ω and 3.0 Ω are in parallel. Find their total resistance.

1/R = 1/6.0 + 1/3.0 = 0.50 Ω−1, so R = 2.0 Ω. This is below the smallest branch resistance, as expected.

Q2. A 1.5 V cell with internal resistance 0.40 Ω supplies a 2.6 Ω load. Calculate current and terminal p.d.

I = ε/(R+r) = 1.5/3.0 = 0.50 A. V = IR = 0.50 × 2.6 = 1.30 V. The lost volts are Ir = 0.20 V.

Q3. A V-against-I graph has intercept 4.5 V and gradient −1.2 V A−1. State ε and r.

From V = ε − Ir: ε = 4.5 V and r = 1.2 Ω.

Q4. An LDR is the bottom resistor of a divider. Explain what happens to Vout as light intensity rises.

The LDR resistance decreases. Since Vout is measured across the LDR, its share of Vin decreases, so Vout decreases.

Q5. Two 1.5 V cells oppose one another in a loop. What is their net e.m.f.?

The sources act in opposite senses, so the net e.m.f. is 0 V. Always inspect polarity rather than automatically adding e.m.f.s.

Which statement must be true for two resistors in parallel?

A calculated divider output is 8.2 V from a 6.0 V supply. What should you do first?

Section 4.3 checklist

  • 4.3.1(a) Apply Kirchhoff’s second law as conservation of energy in electrical circuits.
  • 4.3.1(b) Apply Kirchhoff’s first and second laws to analyse electrical circuits.
  • 4.3.1(c) Calculate total resistance of resistors in series using R = R₁ + R₂ + …
  • 4.3.1(d) Calculate total resistance of resistors in parallel using 1/R = 1/R₁ + 1/R₂ + …
  • 4.3.1(e) Analyse circuits with components including both series and parallel arrangements.
  • 4.3.1(f) Analyse circuits with more than one source of e.m.f.
  • 4.3.2(a) Define source of e.m.f. and internal resistance.
  • 4.3.2(b) Define terminal potential difference and 'lost volts'.
  • 4.3.2(c)(i) Use and apply E = I(R + r) and E = V + Ir for internal resistance.
  • 4.3.2(c)(ii) Use techniques and procedures to determine the internal resistance of a cell or power supply.
  • 4.3.3(a) Describe potential divider circuits with fixed components and potentiometers.
  • 4.3.3(b) Describe potential divider circuits with variable components such as LDRs or thermistors.
  • 4.3.3(c)(i) Use potential divider equations Vout = (R₂ / (R₁ + R₂)) × Vin and V₁ / V₂ = R₁ / R₂.
  • 4.3.3(c)(ii) Use techniques and procedures to investigate potential divider circuits including sensors.

Mastery check

  • Apply both Kirchhoff laws to unfamiliar circuits.
  • Reduce series, parallel and mixed resistor networks.
  • Handle several sources with correct polarity.
  • Calculate and measure e.m.f., terminal p.d. and internal resistance.
  • Design and explain fixed, variable and sensor potential dividers.

Written against the current OCR A Physics A H556 specification. Question structures and misconception prompts are informed by official OCR assessment materials; all questions are original.

Written by: PhysicsUK teaching team

Expertise: Built by a UK A Level Physics teacher and examiner.

Reviewed for: OCR A Level Physics H556

Last reviewed: 2026-07-15

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