Electric Circuits

Circuit Symbols and Diagrams

Standard circuit diagrams use internationally recognised symbols. Key components and their symbols:

Component	Symbol description
Cell	Long line (positive) + short line (negative)
Battery	Multiple cell symbols in series
Switch	Gap that can be bridged
Resistor	Rectangle
Variable resistor	Rectangle with diagonal arrow
Lamp	Circle with cross
Ammeter	Circle labelled A
Voltmeter	Circle labelled V
Fuse	Rectangle with line through it
Diode	Triangle pointing to vertical line

Series Circuits

In a series circuit, components are connected end-to-end in a single loop:

The same current flows through every component.
The total p.d. of the supply equals the sum of the p.d.s across each component.
The equivalent (total) resistance is the sum of all resistances:

$R_s = R_1 + R_2 + R_3 + \ldots$

Removing or breaking any component breaks the entire circuit.

Series circuit diagram: a 6 V battery and switch connected in series with an ammeter (A) and three resistors R1 (2 ohm), R2 (5 ohm), and R3 (10 ohm) in a single loop; a voltmeter (V) is connected in parallel across R2 — Series circuit: the ammeter sits in the main loop (same current everywhere); the voltmeter bridges across R2 only.

Parallel Circuits

In a parallel circuit, components are connected across common junction points (they share the same two nodes):

The p.d. across each branch is the same (equal to the supply p.d.).
The total current from the supply equals the sum of currents through each branch.
The equivalent resistance satisfies:

$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots$

The equivalent resistance of a parallel combination is always less than the smallest individual resistance. Adding more parallel branches reduces the overall resistance.

Parallel circuit diagram: a 6 V battery with an ammeter (A) in the main line connects to two parallel branches, R1 (2 ohm) on top and R2 (5 ohm) below; a voltmeter (V) is connected across both branches — Parallel circuit: the ammeter measures total current from the supply; the voltmeter reads the common p.d. across both branches.

Measuring Current and Voltage

Ammeters measure current and are connected in series with the component being measured (so the same current flows through both).

Voltmeters measure p.d. and are connected in parallel across the component (so they share the same two nodes). A voltmeter must have very high resistance so it does not divert significant current.

ExampleSeries and parallel resistances (2019 Paper 02, Q5)

Three resistors of 2 Ω, 5 Ω, and 10 Ω are connected first in series, then in parallel to a 6 V supply.

Series equivalent resistance:

$R_s = 2 + 5 + 10 = 17 \text{Ω}$

Parallel equivalent resistance:

$\frac{1}{R_p} = \frac{1}{2} + \frac{1}{5} + \frac{1}{10} = \frac{5}{10} + \frac{2}{10} + \frac{1}{10} = \frac{8}{10}$

$R_p = \frac{10}{8} = 1.25 \text{Ω}$

Total current from 6 V supply in parallel circuit:

$I = \frac{V}{R_p} = \frac{6}{1.25} = 4.8 \text{A}$

Cells: Primary and Secondary

Type	Description	Examples
Primary cell	Cannot be recharged, chemical energy converts to electrical energy until exhausted	Zinc-carbon, alkaline batteries
Secondary cell	Can be recharged by passing current through it in reverse	Lead-acid (car battery), lithium-ion (phones)

Cells connected in series add their EMFs. Cells connected in parallel keep the same EMF but can supply more current (longer life).

Exam Tip

For parallel resistance calculations, find $1/R_p$ first by adding the reciprocals, then take the reciprocal of the total. A common error is forgetting to take the final reciprocal.

When two resistors are in parallel, the shortcut formula is: $R_p = \frac{R_1 R_2}{R_1 + R_2}$ .

An ammeter goes in series; a voltmeter goes in parallel. Getting this wrong in a diagram loses marks.

Circuit Symbols and Diagrams

Standard circuit diagrams use internationally recognised symbols. Key components and their symbols:

Component	Symbol description
Cell	Long line (positive) + short line (negative)
Battery	Multiple cell symbols in series
Switch	Gap that can be bridged
Resistor	Rectangle
Variable resistor	Rectangle with diagonal arrow
Lamp	Circle with cross
Ammeter	Circle labelled A
Voltmeter	Circle labelled V
Fuse	Rectangle with line through it
Diode	Triangle pointing to vertical line

Series Circuits

In a series circuit, components are connected end-to-end in a single loop:

The same current flows through every component.
The total p.d. of the supply equals the sum of the p.d.s across each component.
The equivalent (total) resistance is the sum of all resistances:

$R_s = R_1 + R_2 + R_3 + \ldots$

Removing or breaking any component breaks the entire circuit.

Parallel Circuits

In a parallel circuit, components are connected across common junction points (they share the same two nodes):

The p.d. across each branch is the same (equal to the supply p.d.).
The total current from the supply equals the sum of currents through each branch.
The equivalent resistance satisfies:

$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots$

The equivalent resistance of a parallel combination is always less than the smallest individual resistance. Adding more parallel branches reduces the overall resistance.

Measuring Current and Voltage

Ammeters measure current and are connected in series with the component being measured (so the same current flows through both).

ExampleSeries and parallel resistances (2019 Paper 02, Q5)

Three resistors of 2 Ω, 5 Ω, and 10 Ω are connected first in series, then in parallel to a 6 V supply.

Series equivalent resistance:

$R_s = 2 + 5 + 10 = 17 \text{Ω}$

Parallel equivalent resistance:

$\frac{1}{R_p} = \frac{1}{2} + \frac{1}{5} + \frac{1}{10} = \frac{5}{10} + \frac{2}{10} + \frac{1}{10} = \frac{8}{10}$

$R_p = \frac{10}{8} = 1.25 \text{Ω}$

Total current from 6 V supply in parallel circuit:

$I = \frac{V}{R_p} = \frac{6}{1.25} = 4.8 \text{A}$

Cells: Primary and Secondary

Type	Description	Examples
Primary cell	Cannot be recharged, chemical energy converts to electrical energy until exhausted	Zinc-carbon, alkaline batteries
Secondary cell	Can be recharged by passing current through it in reverse	Lead-acid (car battery), lithium-ion (phones)

Cells connected in series add their EMFs. Cells connected in parallel keep the same EMF but can supply more current (longer life).

Exam Tip

For parallel resistance calculations, find $1/R_p$ first by adding the reciprocals, then take the reciprocal of the total. A common error is forgetting to take the final reciprocal.

When two resistors are in parallel, the shortcut formula is: $R_p = \frac{R_1 R_2}{R_1 + R_2}$ .

An ammeter goes in series; a voltmeter goes in parallel. Getting this wrong in a diagram loses marks.