P7: Series and Parallel Circuits
Current, potential difference and resistance rules for series and parallel circuits, plus LDRs and thermistors.
Series Circuits
In a series circuit, components are connected one after the other in a single loop. There is only one path for current to flow.
Series Circuit Rules
- Current is the same through every component
- Potential difference is shared between components
- Resistance adds up — the total resistance is the sum of the individual resistances
- If one component breaks, the whole circuit stops working
Series Resistance
Rtotal = R1 + R2 + R3
The total resistance is always greater than the largest individual resistance.
Worked Example
Three resistors of 4 Ω, 6 Ω and 10 Ω are connected in series to a 20 V supply. Calculate the total resistance and the current in the circuit.
Rtotal = 4 + 6 + 10 = 20 Ω
I = V / R = 20 / 20 = 1 A
Worked Example
Two resistors of 3 Ω and 9 Ω are connected in series to a 12 V supply. Calculate the p.d. across each resistor.
Rtotal = 3 + 9 = 12 Ω
I = V / R = 12 / 12 = 1 A
V1 = IR = 1 × 3 = 3 V
V2 = IR = 1 × 9 = 9 V
Check: 3 + 9 = 12 V (equals the supply voltage)
Parallel Circuits
In a parallel circuit, components are connected on separate branches. There are multiple paths for current to flow.
Parallel Circuit Rules
- Potential difference is the same across each branch
- Current is shared between the branches — the total current equals the sum of the branch currents
- Resistance decreases as more resistors are added in parallel
- If one component breaks, current can still flow through other branches
Parallel Resistance
Adding resistors in parallel always reduces the total resistance. This is because adding another branch provides an extra path for current, making it easier overall for charge to flow.
The total resistance in parallel is always less than the smallest individual resistance.
Worked Example
A 12 V battery is connected across two resistors in parallel: R1 = 6 Ω and R2 = 12 Ω. Calculate the current through each resistor and the total current from the battery.
Each branch has the full 12 V across it:
I1 = V / R1 = 12 / 6 = 2 A
I2 = V / R2 = 12 / 12 = 1 A
Itotal = I1 + I2 = 2 + 1 = 3 A
Comparing Series and Parallel
| Property | Series Circuit | Parallel Circuit |
|---|---|---|
| Current | Same through all components | Splits at junctions; total equals sum of branch currents |
| Potential difference | Shared across components | Same across each branch |
| Adding resistors | Total resistance increases | Total resistance decreases |
| If one component breaks | Whole circuit stops | Other branches still work |
| Everyday use | Fairy lights (old type) | Household wiring |
In exam questions, always start by identifying whether components are in series or parallel, then apply the correct rule for current and potential difference.
LDRs (Light-Dependent Resistors)
An LDR is a resistor whose resistance depends on the intensity of light falling on it.
How an LDR Works
- In bright light, the resistance of an LDR is low
- In darkness, the resistance of an LDR is high
- LDRs are used in automatic lighting systems, burglar alarms and camera shutter controls
Application Example
An LDR is connected in series with a fixed resistor and a power supply. A lamp is connected in parallel with the LDR. In the dark, the LDR resistance is high so it takes a large share of the p.d. The lamp turns on. In bright light, the LDR resistance drops and the lamp turns off. This is the basis of automatic street lighting.
Thermistors
A thermistor is a resistor whose resistance depends on temperature.
How a Thermistor Works
- At high temperatures, the resistance of a thermistor is low
- At low temperatures, the resistance of a thermistor is high
- NTC (negative temperature coefficient) thermistors are the type used at GCSE
- Thermistors are used in temperature sensors, thermostats and electronic thermometers
Application Example
A thermistor is used in a temperature-controlled fan. The thermistor is connected in series with a fixed resistor. When the room gets hot, the thermistor resistance decreases. This increases the p.d. across the fixed resistor, which triggers the fan to turn on. When the room cools, the thermistor resistance increases and the fan switches off.
Sensing Circuits
Sensing circuits use LDRs and thermistors to detect changes in the environment and automatically control devices.
How Sensing Circuits Work
- The sensor (LDR or thermistor) is connected in series with a fixed resistor
- The output component is connected in parallel with one of the resistors
- As conditions change, the sensor resistance changes, altering the p.d. sharing in the circuit
- This changes the p.d. across the output component, turning it on or off
When explaining sensing circuits, always describe what happens to the sensor resistance first, then how this affects the p.d. sharing, then the effect on the output component.
Variable Resistors in Circuits
A variable resistor can be used to control the brightness of a lamp or the speed of a motor by changing the current in the circuit.
Using Variable Resistors
- Increasing the resistance reduces the current, making lamps dimmer or motors slower
- Decreasing the resistance increases the current, making lamps brighter or motors faster
- A variable resistor used in this way is also called a potentiometer
Worked Example
A 6 V battery is connected to a variable resistor and a lamp in series. The lamp has a resistance of 10 Ω. When the variable resistor is set to 20 Ω, calculate the current.
Rtotal = 20 + 10 = 30 Ω
I = V / R = 6 / 30 = 0.2 A
If the variable resistor is reduced to 5 Ω:
Rtotal = 5 + 10 = 15 Ω
I = 6 / 15 = 0.4 A
The current doubles and the lamp becomes brighter.
Practice Questions
1. Two resistors of 8 Ω and 12 Ω are connected in series to a 10 V supply. Calculate the current in the circuit and the p.d. across each resistor.
Rtotal = 8 + 12 = 20 Ω; I = 10 / 20 = 0.5 A; V1 = 0.5 × 8 = 4 V; V2 = 0.5 × 12 = 6 V
2. Two resistors of 10 Ω and 20 Ω are connected in parallel across a 6 V supply. Calculate the total current from the supply.
I1 = 6 / 10 = 0.6 A; I2 = 6 / 20 = 0.3 A; Itotal = 0.6 + 0.3 = 0.9 A
3. Explain why adding a resistor in parallel decreases the total resistance of the circuit.
Adding a parallel branch provides an additional path for current to flow. Even though each path has resistance, the extra path means more total current can flow for the same p.d., so the overall resistance is reduced.
4. Describe how an LDR could be used in an automatic street lamp circuit.
The LDR is connected in series with a fixed resistor and a power supply. In daylight, the LDR has low resistance so the p.d. across it is small and the lamp is off. In darkness, the LDR resistance is high so it takes most of the p.d., and the lamp turns on.
5. A thermistor is at room temperature (20 °C) and has a resistance of 5000 Ω. It is placed in hot water at 80 °C and its resistance drops to 200 Ω. Explain why.
The thermistor is an NTC type. As temperature increases, more charge carriers are released in the semiconductor material. This increases the number of free charge carriers, reducing the resistance.
🔬 Required Practical
Required Practical: Investigating Resistance in Series and Parallel
Aim: To investigate how adding resistors in series and in parallel affects the total resistance of the circuit.
Method: Set up a circuit with a DC power supply, an ammeter in series, and a voltmeter in parallel across the resistors. For the series investigation, start with one resistor and measure the current and p.d. Then add a second identical resistor in series and repeat the measurements. Continue adding resistors in series. For the parallel investigation, start with one resistor, then add a second identical resistor in parallel and measure the total current from the supply and the p.d. across the parallel combination. Continue adding resistors in parallel. Calculate the total resistance for each arrangement using R = V/I.
Variables: Independent: number of resistors and their arrangement (series or parallel). Dependent: total resistance (calculated from V and I). Control: the resistance value of each individual resistor, the supply voltage.
Analysis: In series, adding resistors increases the total resistance. With two identical resistors of resistance R in series, Rtotal = R + R = 2R. In parallel, adding resistors decreases the total resistance. With two identical resistors of resistance R in parallel, Rtotal = R/2. Plot a graph of total resistance against number of resistors for both series and parallel on the same axes.
Common exam questions: "Why does adding a resistor in parallel decrease the total resistance?" — Adding another branch provides an additional path for current to flow. Even though each branch has resistance, having more paths means more total current can flow for the same p.d., so the overall resistance is reduced. "Explain why the total resistance in parallel is always less than the smallest individual resistance." — Because adding the smallest resistance in parallel provides an extra current path, so more current flows than through the smallest resistance alone.
🔢 Maths Skills
Mathematical Skills for this Topic
Adding resistors in series: Rtotal = R1 + R2 + R3. Simply add the values. The total resistance is always greater than the largest individual resistance. For identical resistors: Rtotal = n × R (where n is the number of resistors).
Adding resistors in parallel: 1/Rtotal = 1/R1 + 1/R2. After adding the reciprocals, take the reciprocal of the result to find Rtotal. For two resistors: Rtotal = (R1 × R2) / (R1 + R2). For identical resistors: Rtotal = R/n. The total resistance in parallel is always less than the smallest individual resistance.
Current and voltage calculations in series: In a series circuit, current is the same through all components: I = Vsupply / Rtotal. The p.d. across each resistor is found using V = IR. The p.d. is shared proportionally to resistance — a larger resistor takes a larger share of the p.d. Check your answer: the sum of individual p.d. values must equal the supply voltage.
Current and voltage calculations in parallel: In a parallel circuit, the p.d. is the same across each branch and equals the supply voltage. The current through each branch is found using I = V/Rbranch. The total current is the sum of the branch currents. The current splits inversely proportional to resistance — the branch with less resistance carries more current.
⚠️ Common Misconceptions
Watch Out!
Students often think that voltage is shared equally between components in a series circuit. Wrong: In a series circuit, the voltage is shared equally between all the components. Correct: The p.d. in a series circuit is shared proportionally to the resistance of each component. A larger resistor takes a larger share of the total p.d. Only if the resistors are equal will the p.d. be shared equally. For example, with a 3 Ω and 9 Ω resistor in series across 12 V, the p.d. splits as 3 V and 9 V respectively.
Students often think that current splits equally between parallel branches. Wrong: In a parallel circuit, the current splits equally between each branch. Correct: The current splits inversely proportional to the resistance of each branch. The branch with the lower resistance carries more current. Only if the branches have equal resistance will the current split equally. For example, with a 6 Ω and 12 Ω branch in parallel across 12 V, the 6 Ω branch carries 2 A and the 12 Ω branch carries 1 A — the current is not split equally.
✍️ 6-Mark Question
Extended Answer Question
6 marks: Explain the rules for current and potential difference in series and parallel circuits.
In a series circuit, there is only one path for current to flow, so the current is the same through every component. This is because charge is conserved — the same number of coulombs per second passes through each component. If 2 A flows through one resistor in a series circuit, then 2 A flows through all of them.
In a series circuit, the potential difference is shared between the components. The sum of the p.d. across each component equals the total supply voltage. This is because energy is conserved — the total energy transferred per coulomb by all the components equals the energy supplied per coulomb by the battery. The p.d. is shared in proportion to resistance: V = IR, so for the same current, a larger resistance has a larger p.d. across it.
In a parallel circuit, each branch is connected directly across the supply, so the potential difference is the same across each branch. Each branch has the full supply voltage across it. This is why household appliances connected in parallel all receive 230 V.
In a parallel circuit, the current splits at junctions. The total current from the supply equals the sum of the currents in the individual branches. This is conservation of charge — charge cannot be created or destroyed, so the total flow into a junction equals the total flow out. The current splits inversely proportional to resistance: branches with lower resistance carry more current (I = V/R, and V is the same for each branch).
Mark scheme: 1 mark for series current rule, 1 mark for series p.d. rule with explanation, 1 mark for parallel p.d. rule, 1 mark for parallel current rule, 1 mark for explanation using conservation laws, 1 mark for noting current splits inversely proportional to resistance
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
In the circuit shown, a 12 V battery is connected to two resistors in parallel. R1 = 4 Ω and R2 = 6 Ω. An ammeter reads the total current from the battery.
(a) Calculate the current through each resistor, the total current from the battery, and the total resistance of the circuit.
(b) A third resistor of 12 Ω is added in parallel. Calculate the new total resistance and explain whether this will cause the battery to supply more or less total current.
Answer: (a) Each branch has 12 V across it. I1 = 12/4 = 3 A. I2 = 12/6 = 2 A. Itotal = 3 + 2 = 5 A. Rtotal = V/Itotal = 12/5 = 2.4 Ω. (b) Adding a 12 Ω branch: I3 = 12/12 = 1 A. New Itotal = 5 + 1 = 6 A. New Rtotal = 12/6 = 2.0 Ω. The total resistance has decreased from 2.4 Ω to 2.0 Ω because adding a parallel branch provides another path for current. The battery now supplies more current (6 A instead of 5 A), meaning it will drain faster. This demonstrates that adding resistors in parallel always decreases total resistance and increases the total current drawn from the supply.
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