Grade 8 · Physical Sciences

⚡ Resistors in Electric Circuits

Learn what resistors are, how resistance works, and how to calculate total resistance in series and parallel circuits.

1

What is a Resistor?

Imagine walking through a narrow corridor compared to a wide hallway. The narrow corridor slows you down — it resists your movement. Electricity works in a very similar way. A resistor is a component in an electrical circuit that opposes (resists) the flow of electric current.

Resistors are one of the most common components found in electronic devices — phones, radios, televisions, computers, and countless other gadgets all use them.

Definition: A resistor is an electrical component that limits or controls the amount of current flowing through a circuit.
Resistor symbols and appearance Shows the real-world appearance of a resistor alongside the SA/IEC rectangular symbol and the US zigzag symbol Real resistor (colour bands show value) SA / IEC symbol (rectangle) US / ANSI symbol (zigzag)
Resistor appearance and the two common circuit symbols

What do resistors do in a circuit?

✓ Control current — They limit how much current flows, protecting sensitive components like LEDs from burning out.

✓ Divide voltage — They share voltage between different parts of a circuit.

✓ Set operating conditions — They adjust how other components like transistors and microchips behave.
2

Resistance and Its Units

Resistance is the measure of how much a component opposes the flow of electric current. The greater the resistance, the less current can flow.

Resistance (R) is measured in Ohms (Ω)

The unit Ohm is named after the German physicist Georg Simon Ohm, who discovered the precise relationship between voltage, current, and resistance — a relationship we call Ohm's Law.

Ohm's Law:   V = I × R  |  I = V ÷ R  |  R = V ÷ I
Where: V = Voltage (volts, V)  ·  I = Current (amperes, A)  ·  R = Resistance (ohms, Ω)

Common units of resistance

UnitSymbolEqual toWhere used
OhmΩ1 ΩSmall resistors in everyday circuits
KilohmkΩ1 000 ΩAudio and radio circuits
MegohmMΩ1 000 000 ΩHigh-voltage insulation testing
Ohm's Law triangle Triangle with V at the top, I on the lower left and R on the lower right. Used to recall the three forms of Ohm's Law. V I R Cover V → I × R Cover I → V ÷ R Cover R → V ÷ I Cover the letter you want to find. The rest is the formula.
The Ohm's Law triangle — cover the quantity you want to find
3

Series Connection

When resistors are connected in series, they are joined end-to-end in a single line — like beads on a necklace. The electric current has only one path to follow, so it must pass through every resistor one after the other.

Think of it like this: Three narrow pipes connected one after the other. Water (current) must pass through all three. Each pipe adds to the total resistance the water faces.
Series circuit diagram Three resistors R1 = 4 ohms, R2 = 6 ohms, R3 = 2 ohms connected in series with a battery in a single loop + − Battery R₁ = 4 Ω 4 Ω R₂ = 6 Ω 6 Ω R₃ = 2 Ω 2 Ω Current (I) — one path only
Three resistors in series — the current must pass through each one

Formula — total resistance in series

Rtotal = R₁ + R₂ + R₃ + …

You simply add all the resistances together. For the circuit above:

Rtotal = 4 Ω + 6 Ω + 2 Ω = 12 Ω

Key facts — series

• Current is the same through every resistor

• Voltage is shared (divided) across resistors

• Total R is always greater than any single resistor

Real-life example

Old-style Christmas lights are wired in series. If one bulb blows, the whole string goes out — because the single path is broken!

4

Parallel Connection

When resistors are connected in parallel, they are joined across the same two points, providing multiple paths for the current to flow through. The current splits between the branches.

Think of it like this: Three roads connecting the same two towns. Cars (current) can choose any road. More roads means less overall resistance to traffic flow.
Parallel circuit diagram Three resistors R1 = 3 ohms, R2 = 6 ohms, R3 = 6 ohms connected in parallel with a battery + − Battery R₁ 3 Ω R₂ 6 Ω R₃ 6 Ω Current splits — each branch carries its own portion
Three resistors in parallel — current takes all available paths

Formula — total resistance in parallel

1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + …

Add the reciprocals ("1 divided by" each resistance), then flip the result. For the circuit above (3 Ω, 6 Ω, 6 Ω):

1/Rtotal = 1/3 + 1/6 + 1/6 = 2/6 + 1/6 + 1/6 = 4/6
Rtotal = 6/4 = 1.5 Ω

The total resistance (1.5 Ω) is less than the smallest resistor (3 Ω). This always happens in parallel!

Key facts — parallel

• Voltage is the same across all branches

• Current splits between branches

• Total R is always less than any single resistor

Real-life example

Home electrical wiring is parallel. Each room works independently. If one bulb breaks, the others stay on!

Series vs Parallel — comparison table

FeatureSeriesParallel
Current pathsOne path onlyMultiple paths
Current (I)Same everywhereSplits at junctions
Voltage (V)Shared / dividedSame across all branches
Total resistanceAlways increasesAlways decreases
FormulaR = R₁ + R₂ + …1/R = 1/R₁ + 1/R₂ + …
5

Practice Questions

For each question: first find the total resistance, then use Ohm's Law to calculate the answer. Click Show solution to check your work — but try it yourself first!

Series

Question 1

Two resistors, R₁ = 8 Ω and R₂ = 4 Ω, are connected in series to a 12 V battery. Calculate the current flowing in the circuit.

Step 1 — Find total resistance (series: add them)

Rtotal = R₁ + R₂ = 8 + 4 = 12 Ω

Step 2 — Apply Ohm's Law

I = V ÷ R = 12 V ÷ 12 Ω

∴ I = 1 A

Parallel

Question 2

Two resistors, R₁ = 6 Ω and R₂ = 12 Ω, are connected in parallel across a 6 V battery. Calculate the total current drawn from the battery.

Step 1 — Find total resistance (parallel: use reciprocals)

1/Rtotal = 1/6 + 1/12 = 2/12 + 1/12 = 3/12

Rtotal = 12 ÷ 3 = 4 Ω

Step 2 — Apply Ohm's Law

I = V ÷ R = 6 V ÷ 4 Ω

∴ I = 1.5 A

Series

Question 3

Three resistors of 5 Ω, 10 Ω, and 15 Ω are connected in series. A current of 2 A flows through the circuit. What is the voltage of the battery?

Step 1 — Find total resistance

Rtotal = 5 + 10 + 15 = 30 Ω

Step 2 — Apply Ohm's Law (finding V)

V = I × R = 2 A × 30 Ω

∴ V = 60 V

Parallel

Question 4

Three resistors of 4 Ω, 6 Ω, and 12 Ω are connected in parallel to a 12 V battery. What is the total resistance? How much current does the battery supply?

Step 1 — Find total resistance

1/Rtotal = 1/4 + 1/6 + 1/12 = 3/12 + 2/12 + 1/12 = 6/12

Rtotal = 12 ÷ 6 = 2 Ω

Step 2 — Apply Ohm's Law

I = V ÷ R = 12 V ÷ 2 Ω

∴ Rtotal = 2 Ω  and  I = 6 A

Series — Challenge

Question 5

A 9 V battery is connected to three resistors in series: R₁ = 1 Ω, R₂ = 2 Ω, and R₃ = ?. The current in the circuit is 1.5 A. Find the value of R₃.

Step 1 — Find total resistance using Ohm's Law

Rtotal = V ÷ I = 9 V ÷ 1.5 A = 6 Ω

Step 2 — Solve for R₃

Rtotal = R₁ + R₂ + R₃

6 = 1 + 2 + R₃  →  R₃ = 6 − 3

∴ R₃ = 3 Ω

Parallel — Challenge

Question 6

Two identical resistors are connected in parallel. Their combined resistance is 5 Ω. What is the resistance of each individual resistor?

Key insight: When two equal resistors (each = R) are in parallel:

1/Rtotal = 1/R + 1/R = 2/R   →   Rtotal = R ÷ 2

Solve:

5 = R ÷ 2  →  R = 5 × 2

∴ Each resistor = 10 Ω

Summary
Resistors oppose current flow and are measured in ohms (Ω). In a series circuit, add resistances directly — total resistance goes up. In a parallel circuit, add reciprocals — total resistance goes down. Once you know the total resistance, use Ohm's Law (V = I × R) to find voltage, current, or resistance.