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2.2.3Electricity

Resistors in Series

5 min read 9 parts Lesson 7 of 17 1 quiz

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Section 1 of 9Total resistance in series

When resistors are joined end to end, the current must pass through each one in turn, so the total opposition is greater than any single resistor. The total resistance of resistors in series is the sum of their resistances:

Rtotal = R1 + R2 + R3

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

The unit is ohms (Ω). Adding more resistors in series always increases the total resistance, and the total is larger than the biggest individual resistor.

Real circuits often contain resistors of the standard values 10, 22, 33, 47 and 100 Ω and so on, so you may need to combine two or three in series to obtain a value that is not available. For example, a 68 Ω requirement can be made from 47 Ω and 22 Ω, giving 69 Ω, close enough within the tolerance of the parts.

Section 2 of 9Why the resistances add

The current is the same everywhere in the loop, and the supply p.d. is divided among the resistors: V = V1 + V2 + V3.

Why the resistances add
Using V = IR for each, IRtotal = IR1 + IR2 + IR3.
Dividing by the common current I gives Rtotal = R1 + R2 + R3.
Another way to see it is that joining two wires end to end makes a longer wire, with double the resistance.

Working out the total can also be done in reverse.

Why the resistances add
Given the supply voltage and the current, the total resistance is V/I.
If several resistors are known, the unknown one is found by subtraction.
This two-way working is common in exam questions, and the key is to keep the current constant in series and use V = IR for each part separately.

Section 3 of 9Method for series circuit problems

1
Add the resistors to find the total resistance.
2
Use I = Vsupply / Rtotal to find the current, which is the same everywhere.
3
Use V = IR for each resistor to find individual p.d. values.
4
Check that the individual p.d. values add to the supply voltage.

This method works for any number of resistors, and for components such as lamps that can be treated as resistors at a given operating point.

Be careful to use consistent units; if one resistor is in kΩ, convert it to Ω before adding. A 2.2 kΩ resistor is 2200 Ω. A frequent error is to add 2.2 and 330 without converting.

Section 4 of 9The potential divider

Two resistors in series form a potential divider, giving each a share of the supply p.d. proportional to its resistance. The larger resistor gets the larger p.d. If a fixed resistor is in series with an LDR, as the light level falls the LDR's resistance increases and so does its share of the p.d., which is used in switching circuits.

Section 5 of 9Practical use

Resistors in series are used to reduce the current, for example a 330 Ω resistor in series with an LED protects it from a large current.

Practical use
A variable resistor in series with a lamp can be used as a dimmer: raising its resistance reduces the current and so the brightness.
A series chain of resistors can also provide several different voltages from one battery.

In the dimmer example, as the slider increases the resistance, both the current and the brightness fall, and a larger share of the supply p.d. appears across the variable resistor instead of the lamp. If the total resistance is doubled while the p.d. is unchanged, the current halves. Resistance in series therefore acts as a control on current.

Section 6 of 9Checking with an experiment

Measure the resistance of two resistors separately, then connect them in series and measure again.

Checking with an experiment
Alternatively, use an ammeter and voltmeter to find R = V/I for each and for the combination.
The combined value equals the sum, within the tolerance of the resistors (often ± 5% or ± 10%).
A graph of V against I for the combination is a straight line with a gradient equal to the total resistance.

Section 7 of 9Worked examples

  1. Resistors of 10 Ω, 22 Ω and 33 Ω are in series. Find the total resistance.

  2. A 4.0 Ω resistor and a 8.0 Ω resistor are in series with a 6.0 V battery. Find the current and the p.d. across the 4.0 Ω resistor.

  3. A 12 V supply drives 0.20 A through two series resistors. One is 25 Ω. Find the other.

Section 8 of 9Key terms

TermMeaning
Total resistanceSingle resistance with the same effect as the combination.
Series resistorsResistors joined end to end in one loop.
Potential dividerResistors in series that split voltage.
ToleranceAllowed percentage difference from the marked value.

Section 9 of 9Exam technique

1
Using the parallel rule for series circuits.
2
Forgetting that the current is the same in all series resistors.
3
Thinking the total resistance is less than the largest resistor.
4
Not checking that individual p.d. values add to the supply.
5
Mixing up current and p.d. when solving for a missing resistor.
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