The test circuit
Definition
Variable resistor
A resistor whose resistance can be adjusted to change the current in a circuit.
- To explore how the resistance of a component behaves, the circuit must let you change the current through the component and measure both the current and the potential difference at each setting.
- Each part of the standard test circuit has its own job.
- d.c. power supply or battery: provides the potential difference that drives the current.
- Component under test: the wire, lamp, diode, thermistor or LDR being investigated.
- Ammeter in series with the component: measures the current through it.
- Voltmeter in parallel across the component only: measures the potential difference across it, without including the ammeter or any other part.
- Variable resistor in series: changes the current, and so changes the potential difference across the component.
- Switch: lets the current be turned off between readings so that the component does not heat up.
- Turning the variable resistor to a larger resistance gives a smaller current and a smaller potential difference across the component, while a smaller setting gives a larger current.
- A variable power supply can be used instead of a variable resistor, by changing its output in steps.
- To take readings for current in the opposite direction, the connections to the supply are reversed, and the readings are recorded as negative values.
Planning the investigation
Definition
Independent variable
The variable that is deliberately changed in an investigation.
Definition
Dependent variable
The variable that is measured to find out how it is affected by the independent variable.
Definition
Control variable
A variable that is kept the same throughout an investigation so that it cannot affect the results.
- The independent variable is usually the potential difference across the component, which you change in steps.
- The dependent variable is the current through the component, which you measure at each step.
- The control variables must be kept the same so that only the potential difference affects the current.
- For a metal wire, the control variables are its length, thickness, material and temperature.
- For an NTC thermistor, the temperature must be held constant at each setting, and for an LDR the light intensity must be held constant.
- Take at least five or six readings spread evenly across the range, plus the same number in the reverse direction when the component might behave differently each way.
- Repeat each reading and calculate a mean, ignoring any result that is clearly anomalous.
Adapting the circuit for each component
- Wire of varying resistance: a length of resistance wire is fixed along a metre rule, and a sliding crocodile clip selects how much of it is in the circuit.
- The voltmeter is connected across the selected length only, and the current is kept small so the wire does not warm up.
- Filament lamp: the potential difference is increased in steps up to the rated value printed on the lamp, and each reading is taken once the brightness has settled.
- Diode: a protective resistor is placed in series with the diode, because a diode in the forward direction has a very small resistance and could otherwise carry a damaging current.
- The readings are taken in small steps around 0.6 V0.6\ \text{V}0.6 V, where the current starts to rise sharply, and the supply is then reversed to test the other direction.
- NTC thermistor: the thermistor is placed in a beaker of water with a thermometer, so its temperature can be changed and measured while the same measuring circuit records the current and potential difference.
- LDR: the LDR is placed at a measured distance from a lamp in a darkened room, so the light intensity on it can be changed by moving the lamp while the circuit records the current and potential difference.
Using the readings
- For each pair of readings, calculate the resistance using R=VIR = \dfrac{V}{I}R=IV.
- Comparing the resistance values shows whether the resistance is constant or changes as the current changes.
- Plotting the current against the potential difference shows the same pattern as a graph, which is the clearest way to compare components.
Example
Choosing a protective resistor
- A diode must not carry more than 0.10 A0.10\ \text{A}0.10 A, and it is connected in series with a protective resistor to a 6.0 V6.0\ \text{V}6.0 V supply.
- When the diode conducts, it has about 0.7 V0.7\ \text{V}0.7 V across it, so the rest of the supply potential difference is across the resistor.
- The smallest resistance that keeps the current at or below 0.10 A0.10\ \text{A}0.10 A is found from R=VIR = \dfrac{V}{I}R=IV.
- A protective resistor of 100 Ω100\ \Omega100 Ω would therefore be a safe choice, because it gives a current of about 0.05 A0.05\ \text{A}0.05 A.
Practical
Wire thickness and resistance
- Aim: to investigate how the thickness of a metal wire affects its resistance.
- Apparatus: five constantan wires of the same length, 50.0 cm50.0\ \text{cm}50.0 cm, with different diameters, a micrometer, a power supply set to 2 V2\ \text{V}2 V, a variable resistor, a switch, a digital ammeter, a digital voltmeter and crocodile-clip leads.
- Method, preparing the wires:
- Measure the diameter of each wire with the micrometer at three places along its length and calculate a mean.
- Mark a 50.0 cm50.0\ \text{cm}50.0 cm length on each wire with tape so the same length is tested every time.
- Method, taking readings:
- Connect the supply, switch, variable resistor, ammeter and the first wire in series, with the voltmeter across the marked length only.
- Adjust the variable resistor so the current is about 0.2 A0.2\ \text{A}0.2 A, close the switch, record the current and potential difference, and open the switch.
- Repeat with each wire in turn, then repeat the full set twice more and calculate a mean resistance for each wire using R=VIR = \dfrac{V}{I}R=IV.
- Variables: the independent variable is the diameter of the wire, the dependent variable is its resistance, and the control variables are the length, the material and the temperature of the wire.
- Results: the thinnest wire has the largest resistance, and the resistance falls as the diameter increases.
- Conclusion: a thicker wire of the same length and material has a smaller resistance, because the electrons have more room to pass between the ions.
- Watch out: keep the current small and the switch closed only briefly, because a warm wire has a higher resistance and would distort the comparison.
- Safety: thin wires heat up quickly, so let each wire cool before handling it and keep the supply potential difference low.
Common Mistake
- Do not connect the voltmeter across both the component and the ammeter, because it would then measure the wrong potential difference.
- Do not leave out the protective resistor when testing a diode, because the current could become large enough to damage the diode or the meters.
- Do not change two things at once, such as the potential difference and the temperature of a thermistor, because you cannot then tell which one caused the change in current.
Exam technique
Explaining circuit designs
- When you are asked to explain the design of a circuit, name each component and give its purpose, such as the variable resistor changes the current through the component.
- State where each meter goes and why, so write that the ammeter is in series to measure the current through the component and the voltmeter is in parallel to measure the potential difference across it.
- Finish by saying how the readings are used, which is to calculate R=VIR = \dfrac{V}{I}R=IV for each pair or to plot current against potential difference.
Self review
- State the purpose of the variable resistor in a circuit used to test a component.
- Explain why a protective resistor is used when testing a diode.
- Describe how the circuit is changed to obtain negative readings of current and potential difference.
- Name two control variables when investigating the resistance of a metal wire.
- Describe how the light intensity on an LDR can be changed in an investigation.
