☰ Year plan · Science

Electric circuits: Ohm’s law, resistors and the cost of electricity

Week 8 · Lesson 2 Electric Circuits: Ohm's law, resistors in series and in parallel, electric power and energy, the cost of household electricity, safety · 3 lessons
2

Resistors in series and in parallel

Science Prep 3 Term 1, Unit 2: pp. 46–53
GoalFind the equivalent resistance of identical resistors in series and in parallel and say what is the same and what divides in each.
New words
equivalent resistance · the single resistance that has the same effect on the circuit as a group of resistorsseries circuit · components joined one after another in a single loop, so the same current passes through eachparallel circuit · components joined side by side across the same two points, so each has the same voltage
Explanation

A group of resistors can be replaced by one equivalent resistance. For n identical resistors R in series, the current is the same in each, the voltage divides equally and Req = n × R, which is greater than one resistor; it is used to get a large resistance. For n identical resistors R in parallel, the voltage across each is the same, the current divides equally and Req = R ÷ n, which is smaller than one resistor. The equivalent resistance in parallel is always smaller than the smallest branch. In series, the current is the same everywhere; in parallel it is the voltage that is the same. Household appliances are joined in parallel, so each one works on its own at the full voltage, and the others carry on if one is switched off or breaks. If one bulb in a series string breaks, the loop is open and all the bulbs go out. A pacemaker is a small device with a battery, a microchip and wires to the heart muscle, which sends small pulses when the heartbeat becomes irregular; it is a reminder that circuits are used to help people.

Identical resistors R, n of themSame in eachDividesReq
seriescurrentvoltagen × R
parallelvoltagecurrentR ÷ n
Worked examples
6 V+−4 Ω4 Ω4 Ω
Three 4 Ω resistors in series: Req = 3 × 4 Ω = 12 Ω. Joined to a 6 V source: I = 6 V ÷ 12 Ω = 0.5 A in each. The voltage across each is V = 0.5 A × 4 Ω = 2 V, and 3 × 2 V = 6 V.
4 Ω4 Ω4 Ω6 V+−
The same three resistors in parallel across 6 V: each has 6 V across it, so each carries 6 V ÷ 4 Ω = 1.5 A. The total current is 3 × 1.5 A = 4.5 A. Equivalent resistance = 4 Ω ÷ 3 ≈ 1.33 Ω; check: 6 V ÷ 1.33 Ω ≈ 4.5 A. Req is less than 4 Ω, the smallest branch.
Two 10 Ω resistors: in series 2 × 10 Ω = 20 Ω; in parallel 10 Ω ÷ 2 = 5 Ω. The parallel value is smaller than 10 Ω, and the series value is larger.
A string of 4 identical lamps in series loses all its light when one lamp is removed. Four lamps in parallel: removing one leaves the other three lit. This is why homes use parallel circuits.
Class activity

Two bulbs and one cell, with a grown-up. Make a series circuit of two small bulbs and one 1.5 V cell: unscrew one bulb and describe what the other does. Then make a parallel circuit and repeat. Fill a table: series against parallel (what the other bulb does, brightness, what is the same). Draw both circuits with symbols. Use 1.5 V only, never the mains or a charger.

Practice
1
Four 5 Ω resistors are in series. Find Req.
2
Four 8 Ω resistors are in parallel. Find Req.
3
Three identical resistors in series are joined to 12 V and the current is 1 A. Find the voltage across one resistor and the resistance of each.
4
In which circuit is the voltage the same across every resistor: series or parallel?
5
Two 6 Ω resistors are in parallel across 12 V. Find the current in each and the total current.