10.18–10.21Resistors
You should be able to explain that, for some resistors, the value of R remains constant, but that in others it can change as the current changes.
The current through an ohmic conductor at a constant temperature is directly proportional to the potential difference across the resistor. This means that the resistance remains constant as the current changes.
The resistance of components such as lamps, diodes, thermistors and LDRs is not constant; it changes with the current through the component.
The applications are examinable. A thermistor in a thermostat: as the room warms, the thermistor's resistance falls, the circuit detects the change and switches the heater off. An LDR switching lights on when it gets dark: as the light fades, the LDR's resistance rises, and the circuit switches the lamp on.
You should be able to explain the design and use of a circuit to measure the resistance of a component, by measuring the current through and the potential difference across the component, and to draw an appropriate circuit diagram using correct circuit symbols. You should also be able to use graphs to explore whether circuit elements are linear or non-linear, and relate the curves produced to their function and properties.
Required practical 4
Investigate the I–V characteristics of a variety of circuit elements
- Connect the component in series with an ammeter and a variable resistor, with a voltmeter across the component.
- Use the variable resistor to set a series of potential differences, recording the current at each.
- Reverse the connections to the power supply and repeat, so the graph covers negative values as well.
- Plot current on the vertical axis against potential difference on the horizontal axis.
- For the diode, add a protective resistor in series, because a forward-biased diode has almost no resistance of its own.
- For the resistor, take readings quickly and switch off between them, so its temperature stays constant.
Common mistake
A curved I–V graph does not mean the component is broken or the readings are wrong. It means the resistance changes — which is exactly what a filament lamp is expected to do.
- Ohmic conductor
- a conductor in which the current at constant temperature is directly proportional to the potential difference, so its resistance remains constant as the current changes
10.14Why the total resistance changes
You should be able to explain qualitatively why adding resistors in series increases the total resistance, whilst adding resistors in parallel decreases the total resistance.
In series, the charge has to pass through every resistor in turn. Each one opposes the flow, so adding another adds its opposition to the total — the current has more to get through and the total resistance rises.
In parallel, each new resistor provides another separate path for the charge to take. More paths means more charge can flow in total for the same potential difference, so the total current rises and the total resistance falls.
That is why the parallel total is less than the smallest individual resistor: adding a path can only ever make it easier for charge to flow, never harder — even if the new path is a poor one.
Common mistake
In parallel the total resistance is not the average of the two, and it is not somewhere between them. It is always less than the smaller one. If your answer for two 10 Ω resistors in parallel is more than 5 Ω, something is wrong.
10.15–10.17Calculations in series circuits
You should be able to calculate the currents, potential differences and resistances in dc series circuits, and to solve problems for circuits which include resistors in series using the concept of equivalent resistance.
You are not required to calculate the total resistance of two resistors joined in parallel — so a parallel calculation will only ever ask for currents and potential differences, using the two rules above.
Equivalent resistance means replacing several series resistors with a single one of the same total value, so that V = I R can be applied to the whole circuit at once.
Worked example
A 6.0 V supply is connected in series with a 4.0 Ω and an 8.0 Ω resistor. Calculate the current, and the potential difference across each resistor.
- Find the equivalent resistance: Rtotal = R1 + R2 = 4.0 + 8.0 = 12.0 Ω.
- Apply V = I R to the whole circuit: I = V ÷ R = 6.0 ÷ 12.0 = 0.50 A.
- In series the current is the same through each component, so 0.50 A flows through both.
- Across the 4.0 Ω resistor: V = I R = 0.50 × 4.0 = 2.0 V.
- Across the 8.0 Ω resistor: V = 0.50 × 8.0 = 4.0 V.
- Check: 2.0 + 4.0 = 6.0 V, which is the supply — the potential difference is shared, as it must be.
Answer: 0.50 A throughout; 2.0 V across the 4.0 Ω resistor and 4.0 V across the 8.0 Ω resistor.
Worked example
Two lamps are connected in parallel across a 12 V supply. One draws 0.30 A and the other 0.50 A. State the potential difference across each lamp and calculate the total current from the supply.
- In parallel the potential difference across each component is the same as the supply.
- So each lamp has 12 V across it.
- The total current through the whole circuit is the sum of the currents through the separate components.
- 0.30 + 0.50 = 0.80 A.
Answer: 12 V across each lamp, and a total supply current of 0.80 A.
You should also be able to explain the design and use of dc series circuits for measurement and testing purposes.
A series circuit is used for testing because the single current makes the readings unambiguous: one ammeter anywhere in the loop measures the current through everything, and adding a variable resistor in series controls that current for every component at once. That is exactly the arrangement used in required practicals 3 and 4.
Common mistake
Check that the potential differences across series components add up to the supply. It is a free check on the whole calculation, and it catches an arithmetic slip immediately.
Before you practise
- potential difference = current × resistance.
- A fixed resistor at constant temperature gives a straight line through the origin on an I-V graph.
- A filament lamp curves, because it heats up and its resistance rises.
- A diode lets current flow in one direction only, so its graph is flat then rises sharply.
- An LDR's resistance falls as light intensity rises; a thermistor's falls as temperature rises.
- Resistors in series: add the resistances, so the total is always greater than either.
- Resistors in parallel: the total is less than the smallest of them, because there are more paths for the current.
- In series the current is the same and the potential differences add; in parallel the potential difference is the same and the currents add.