Resistance and circuit components
What you'll learn
- How to calculate current, potential difference and resistance in series circuits
- How to set up circuits to measure current and potential difference safely
- How fixed resistors, filament lamps, diodes, LDRs and thermistors behave
- Why resistors heat up, and when that heating is useful or unwanted
The basic circuit quantities
Electrical circuits involve moving charge. To understand resistance, you need three quantities: current, potential difference and resistance.
Current, potential difference and resistance
- Electric current, III, is the rate of flow of electric charge. It is measured in amperes (A).
- Potential difference, VVV, is the energy transferred per unit charge between two points. It is measured in volts (V).
- Resistance, RRR, is how much a component opposes the flow of current. It is measured in ohms (Ω).
The key relationship is:
V=IRV = I RV=IRYou can rearrange it as:
R=VII=VRR = \frac{V}{I} \qquad I = \frac{V}{R}R=IVI=RVCalculating resistance
A resistor has a potential difference of 6.0 V across it and a current of 0.30 A through it. Find its resistance.
- Choose the form that gives resistance: R=VIR = \frac{V}{I}R=IV.
- Substitute the values, keeping the units consistent: R=6.0 V0.30 AR = \frac{6.0\text{ V}}{0.30\text{ A}}R=0.30 A6.0 V.
- Calculate the result: R=20 ΩR = 20\ \OmegaR=20 Ω.
Series circuits
A series circuit has components connected one after another in a single loop. There is only one path for the current.
Series circuit rules
- The current is the same at every point in a series circuit.
- The potential differences across components add up to the supply potential difference.
- The total resistance is the sum of the individual resistances: Rtotal=R1+R2+R3+…R_\text{total} = R_1 + R_2 + R_3 + \dotsRtotal=R1+R2+R3+…
If you add more resistors in series, the total resistance increases, so the current from the same battery decreases.
Finding current and potential differences in series
A 12 V battery is connected to two resistors in series: 4 Ω and 8 Ω. Find the current and the potential difference across each resistor.
- Add the series resistances: Rtotal=4 Ω+8 Ω=12 ΩR_\text{total} = 4\ \Omega + 8\ \Omega = 12\ \OmegaRtotal=4 Ω+8 Ω=12 Ω.
- Use the total resistance to find the circuit current: I=VR=12 V12 Ω=1.0 AI = \frac{V}{R} = \frac{12\text{ V}}{12\ \Omega} = 1.0\text{ A}I=RV=12 Ω12 V=1.0 A.
- Use V=IRV = I RV=IR for each resistor: the 4 Ω resistor has V=1.0 A×4 Ω=4 VV = 1.0\text{ A} \times 4\ \Omega = 4\text{ V}V=1.0 A×4 Ω=4 V, and the 8 Ω resistor has V=1.0 A×8 Ω=8 VV = 1.0\text{ A} \times 8\ \Omega = 8\text{ V}V=1.0 A×8 Ω=8 V.
- Check the potential differences add to the supply: 4 V plus 8 V gives 12 V.
Adding currents in series
Do not split or add the current in a series circuit. The current is the same through every component because there is only one route for the charge.
Measuring current and potential difference
An ammeter measures current and is connected in series with the component. A voltmeter measures potential difference and is connected in parallel, meaning it is connected across the two sides of the component.
A variable resistor is an adjustable resistor. In the core practical, it lets you change the current and potential difference so you can collect several readings for an I-V graph.
This circuit is used to investigate how current varies with potential difference for different test components.
Placing meters in a component test
You want to test a filament lamp and measure the current through it and the potential difference across it.
- Put the ammeter in series with the lamp, because it must measure the same current that passes through the lamp.
- Put the voltmeter in parallel across the lamp, because potential difference is measured between the two ends of a component.
- Put a variable resistor in series as well, so you can change the current and collect a range of readings.
For the core practical, you build the circuit, record pairs of current and potential difference readings, then adjust the variable resistor and repeat. You can swap the test component for a fixed resistor, filament lamp or diode. To get negative readings, reverse the battery connections.
Good practical habits
Use a low current at first, switch off between readings if components get hot, and repeat readings if something looks odd. For a diode, use a protective resistor so the current does not become too large.
I-V characteristics
An I-V characteristic is a graph showing how current III changes with potential difference VVV for a component. Current is usually on the vertical axis and potential difference on the horizontal axis.
Fixed resistor
A fixed resistor has a resistance that stays constant, as long as its temperature stays constant. Its I-V graph is a straight line through the origin.
This means current is directly proportional to potential difference.
Filament lamp
A filament lamp contains a thin wire filament that gets hot and glows. As the current increases, the filament gets hotter. Its resistance increases, so the current rises less quickly.
That is why the graph curves and becomes less steep at higher potential differences.
Diode
A diode allows current to flow much more easily in one direction than the other. In the forward direction, it conducts once the potential difference is large enough. In the reverse direction, the current is almost zero.
Graph gradient and resistance
On an I-V graph with current on the vertical axis, the gradient is I÷VI \div VI÷V, not RRR. For a fixed resistor, resistance is found using R=VIR = \frac{V}{I}R=IV from a point on the line.
Finding resistance from an I-V graph
A point on a fixed resistor’s I-V graph has potential difference 5.0 V and current 0.25 A. Find the resistance.
- Use a point on the straight line because the resistor has constant resistance.
- Apply R=VIR = \frac{V}{I}R=IV using the graph values: R=5.0 V0.25 AR = \frac{5.0\text{ V}}{0.25\text{ A}}R=0.25 A5.0 V.
- Calculate the resistance: R=20 ΩR = 20\ \OmegaR=20 Ω.
LDRs and thermistors
A light-dependent resistor, or LDR, is a resistor whose resistance changes with light intensity. In bright light, its resistance is low. In darkness, its resistance is high.
A thermistor is a resistor whose resistance changes with temperature. For GCSE, you need the negative temperature coefficient thermistor, often shortened to NTC thermistor. Its resistance decreases as temperature increases.
To investigate an LDR, place it in the measuring circuit and change the light intensity, for example by moving a lamp different distances away. To investigate a thermistor, place it in a water bath and change the temperature while measuring current and potential difference.
Sensors change resistance
LDRs and thermistors are useful because a change in the environment causes a change in resistance, which changes current and potential difference in a circuit.
Heating effect of current
When there is an electric current in a resistor, the resistor heats up. This is an energy transfer: electrical energy is transferred to thermal energy.
Dissipated energy
When energy is dissipated, it is transferred to the surroundings, usually becoming less useful. In resistors, electrical energy is often dissipated as thermal energy.
Inside a metal resistor, electrons move through a lattice of positive ions. The ions are not free to flow around; they vibrate about fixed positions. As electrons move through the resistor, they collide with these ions and transfer energy to them. The ions vibrate more, so the resistor gets hotter.
Why resistance causes heating
Electrical current does work against resistance. The energy transferred by the moving electrons is passed to the lattice ions during collisions, increasing the thermal energy of the resistor and surroundings.
Energy is not destroyed
Do not say resistance “uses up” or “destroys” energy. Energy is transferred, often into thermal energy that spreads into the surroundings.
Useful and unwanted heating
The heating effect of current can be useful. Electric heaters, kettles, toasters and hairdryers are designed to transfer electrical energy into thermal energy. A fuse also uses heating: if the current is too large, the fuse wire melts and breaks the circuit.
But heating can also be a disadvantage. Wires and components may waste energy as thermal energy, reducing efficiency. Overheating can damage components or become a fire risk.
If you are sitting Higher Tier, you may also need to explain how unwanted energy transfer can be reduced by using low-resistance wires. For the same current, lower resistance means less heating in the wires. This can be achieved by using short, thick wires made from good conductors such as copper, and by making secure low-resistance connections.
Choosing a wire to reduce heating
Two wires carry the same current. Wire A has a resistance of 0.50 Ω and wire B has a resistance of 0.10 Ω.
- For the same current, heating power increases with resistance, often summarised by P=I2RP = I^2RP=I2R.
- Compare the resistances: wire B has one fifth of the resistance of wire A.
- Choose wire B, because it will dissipate less energy as thermal energy each second.
In the exam
- For series calculations, write the three rules first: same current, potential differences add, resistances add.
- For practical circuit questions, remember: ammeter in series, voltmeter in parallel across the component.
- For I-V graphs, link the shape to resistance: straight line means constant resistance; curves mean resistance is changing.
Check yourself
- In a series circuit with two resistors, what happens to the total resistance when a third resistor is added?
- Why does a filament lamp’s resistance increase as the current increases?
- How do the resistances of an LDR and an NTC thermistor change in bright light and at high temperature?
