19.3 Series and Parallel Circuits — American System Physics Revision Notes & Topical Questions

Part 1 of 7Key ideas

Key ideas

Series current

I is the same everywhere in a single loop.

Series p.d.: V_supply = V₁ + V₂ + … (V).

Series resistance

R_T = R₁ + R₂ + … (Ω).

Parallel current

I_T = I₁ + I₂ + … (A) — current into a junction = current out.

Parallel p.d.: the p.d. across each branch is the same.

Parallel resistance

1/R_T = 1/R₁ + 1/R₂ + …; two resistors: R_T = R₁R₂/(R₁ + R₂).

Potential divider

V_out = V_in × R₂/(R₁ + R₂); also V₁/V₂ = R₁/R₂.

Fuse rating

Fuse rating find I = P/V and choose the next rating above it.

n identical resistors R in parallel: R_T = R/n.

Part 2 of 7Learning objectives

1

State the rules for current, p.d. and resistance in series and parallel circuits.

2

Calculate combined resistance for series and parallel combinations.

3

Explain the advantages of parallel wiring for lighting and appliances.

4

Use a potential divider and explain its use with thermistors and LDRs.

5

Describe the hazards of mains electricity and the safety features used.

Part 3 of 7Essential knowledge

1

19.3 Series and Parallel Circuits concept map: Series current, Series resistance, Parallel current, Parallel resistance, Potential divider — Visual guide to the key ideas explained in this lesson.

2

In a series circuit there is one path, so each coulomb passes through every component; the current is the same everywhere.

3

The energy given to each coulomb by the source is shared between the series components, so the p.d.s add up to the e.m.f. (conservation of energy).

4

Adding a resistor in series increases the total resistance, so the current decreases.

5

In parallel, the current divides at a junction; charge is conserved, so the sum of branch currents equals the supply current. The branch with the smaller resistance carries the larger current.

6

Each parallel branch is connected directly across the supply, so each has the same p.d.

7

Adding another resistor in parallel provides an extra path for charge, so the combined resistance decreases and the total current from the supply increases.

8

Parallel wiring in homes means every appliance receives the full mains p.d., each can be switched independently, and one failing does not switch off the others.

9

A potential divider with a thermistor or LDR produces an output p.d. that changes with temperature or light. The larger resistor always has the larger share of the p.d.; e.g. with an LDR as R₂, darkness raises R₂ and so raises V_out, which can switch on a lamp.

10

Hazards of mains electricity include damaged insulation, overheated cables (too much current for the cable) and damp conditions (water conducts and can create a path through a person).

11

A fuse is placed in the live wire. If a fault makes the casing live, current flows through the earth wire, the current surges and the fuse melts, disconnecting the appliance from the live supply.

12

Switches and fuses must be in the live wire so that, when open, the appliance is not connected to the high p.d.

13

Short circuits have very low resistance, so I = V/R becomes very large, causing rapid heating.

Part 4 of 7Process & sequence

1

Draw the circuit and identify which resistors are in series and which are in parallel.

2

What the symbols mean:

Combine parallel groups: 1/R = 1/R₁ + 1/R₂ (or R₁R₂/(R₁+R₂) for two).

What the symbols mean: R_T = total resistance of resistors in parallel (Ω), always smaller than the smallest one · R₁, R₂ = the separate resistances (Ω)

3

What the symbols mean:

Add series resistances: R = R₁ + R₂ + ….

What the symbols mean: R_T = total resistance of resistors in series (Ω) · R₁, R₂ = the separate resistances (Ω)

4

Find the total current from the supply: I = V/R_total.

5

Find the p.d. across each series part using V = IR; the p.d.s add up to the supply p.d.

6

Find the current in each parallel branch using I = V/R; the branch currents add to the total current.

7

Check: total power = sum of powers in each resistor.

How the earth wire and fuse prevent electric shockwrite these steps in this order; each step is a marking point.

1

A fault causes the live wire to touch the metal casing.

2

The casing becomes live, but it is connected to earth by the low-resistance earth wire.

3

A very large current flows from live, through the casing and earth wire, to the ground.

4

The large current makes the fuse wire heat up and melt (or trips the circuit breaker).

5

The live supply is disconnected, so the casing is safe to touch.

Part 5 of 7Worked examples

3.0 Ω

A 4.0 Ω and a 12 Ω resistor are connected in parallel across a 6.0 V battery. Find (a) the combined resistance, (b) the total current, (c) the current in the 4.0 Ω resistor.

(a) R = (4.0 × 12)/(4.0 + 12) = 48/16 = 3.0 Ω.
- (b) I = V/R = 6.0/3.0 = 2.0 A.
- (c) I₁ = 6.0/4.0 = 1.5 A .
  - (the 12 Ω carries 0.50 A; 1.5 + 0.50 = 2.0 A ✓)

0.30 A

A 10 Ω resistor and a 20 Ω resistor are in series with a 9.0 V supply. Find the current and the p.d. across each resistor.

R_T = 10 + 20 = 30 Ω.
- I = 9.0/30 = 0.30 A.
- V₁₀ = 0.30 × 10 = 3.0 V;
  - V₂₀ = 0.30 × 20 = 6.0 V;
  - 3.0 + 6.0 = 9.0 V ✓.

13 A

A 2.0 kW heater runs from a 230 V supply. Fuses of 3 A, 5 A, 13 A are available. Which should be used?

I = P/V = 2000/230 = 8.7 A. The fuse must be just above this: 13 A.

Part 6 of 7Summary

1

In series, current is the same and p.d.s add.

2

In parallel, p.d. is the same across each branch and currents add.

3

Series resistances add; parallel combined resistance is less than the smallest.

4

A potential divider shares the supply p.d. in the ratio of the resistances.

5

Fuses and circuit breakers protect against excessive current; the earth wire protects against electric shock.

Part 7 of 7Compare: Compare

Series versus parallel
Property	Series	Parallel
Current	Same at every point: I = I₁ = I₂	Splits between branches: I = I₁ + I₂
p.d.	Shared: V = V₁ + V₂	Same across each branch: V = V₁ = V₂
Combined resistance	R = R₁ + R₂ (larger than any one)	1/R = 1/R₁ + 1/R₂ (smaller than the smallest)
If one lamp fails	All lamps go out	Other lamps stay on
Uses	Fairy lights, potential dividers	House wiring; each appliance gets full p.d. and its own switch

Mains safety features
Feature	What it does	Protects
Fuse	Melts if current too high	Wiring/appliance from overheating and fire
Circuit breaker	Trips if current too high; resettable	Wiring from overheating
Earth wire	Gives low-resistance path from casing to ground	User from electric shock
Double insulation	Plastic casing that cannot become live	User from electric shock

Choose a fuse rating slightly above the normal operating current (I = P/V).

Key terms

Command terms

Identify / Describe (FRQ)

A short, specific statement; describing requires relevant characteristics, not a single word.

Explain / Justify (FRQ)

Give the cause-and-effect reasoning or evidence; a restated fact does not score.

Calculate

Show setup, substitution and the answer with units.

Predict

State the expected outcome; add a reason only if asked to justify.

MCQ technique

Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Exam technique

Keywords the mark scheme looks for in this lesson

Series circuit · Parallel circuit · Junction · Combined (equivalent) resistance · Potential divider · Short circuit · Fuse · Circuit breaker · Earth wire · Double insulation · Live, neutral wires · Switch

Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1

Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).

2

Use precise vocabulary, never “it/stuff/things”.

3

Show units and working in calculations.

4

In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1

current is shared in a series circuitthe current is the same at all points in series; the p.d. is shared.

2

adding resistors in parallel increases resistanceadding a parallel branch decreases the combined resistance.

3

the fuse stops you getting a shockthe earth wire and fuse together disconnect the supply; the fuse alone protects against overheating from excessive current.

4

the fuse blows when there is a lot of voltagethe fuse melts when the current exceeds its rating.

5

the earth wire takes the electricity awaythe earth wire provides a low-resistance path so a large current flows and blows the fuse.

Series and Parallel Circuits — American System Physics Revision Notes & Topical Questions