Resistance measures how hard a component makes it for charge to flow
Definition
Resistance
The ratio of the potential difference across a component to the current through it, measured in ohms, Ω\OmegaΩ.
R=VI R = \frac{V}{I} R=IV- Put the same p.d. across two different components and the one that lets less current through has the greater resistance.
- The unit is the ohm, symbol Ω\OmegaΩ, and 1 Ω1\ \Omega1 Ω means 1 V1\ \text{V}1 V is needed to drive 1 A1\ \text{A}1 A through the component.
- Resistance comes from the free electrons colliding with the vibrating positive ions as they drift, which passes energy to the lattice and warms the component.
- Typical values give a feel for the scale: connecting leads well under 1 Ω1\ \Omega1 Ω, a torch bulb a few ohms, and a resistor on a circuit board a few hundred ohms.
- The rearranged forms V=IRV = IRV=IR and I=VRI = \dfrac{V}{R}I=RV are used just as often, so learn all three together.
- Because I=VRI = \dfrac{V}{R}I=RV, doubling the resistance at a fixed p.d. halves the current.
Measuring resistance needs one ammeter, one voltmeter and one division
- Resistance is not read off a single meter here: you measure VVV and III and then calculate.
- The ammeter goes in series with the component, so that the current through the meter is the current through the component.
- The voltmeter goes in parallel across the component, so that it reads the p.d. between its two ends.
- A variable resistor in series lets you change the current, so several pairs of readings can be taken instead of relying on one.
- Calculate R=VIR = \dfrac{V}{I}R=IV for each pair and average, which limits the damage done by any single poor reading.
- Plotting III against VVV is the stronger treatment, because the gradient of the best-fit line equals 1R\dfrac{1}{R}R1 and every reading contributes to the answer.
Practical
Investigation: measuring the resistance of a wire
- Aim: to measure the resistance of a wire from readings of current and potential difference, and to see how it depends on the wire's length and thickness.
- Apparatus: a battery, an ammeter, a voltmeter, a variable resistor, constantan wire of two different diameters, a metre rule, crocodile clips, a switch and connecting leads.
- Method:
- Tape the test wire alongside a metre rule, pulled straight, and clip one crocodile clip at the zero mark.
- Connect the battery, switch, variable resistor, ammeter and test wire in one series loop, then connect the voltmeter across the length of test wire in use.
- Clip the second crocodile clip at 20.0 cm20.0\ \text{cm}20.0 cm and close the switch only long enough to read both meters, then open it again.
- Move the variable resistor to a new setting and take a second and a third pair of readings at the same length.
- Calculate R=V/IR = V/IR=V/I for each pair and average them.
- Move the second clip to 40.040.040.0, 60.060.060.0, 80.080.080.0 and 100.0 cm100.0\ \text{cm}100.0 cm in turn and repeat the whole set of readings at each length.
- Swap in the thicker constantan wire and repeat at one fixed length, so that the cross-sectional area is the only thing that has changed.
- Measure and plot: record the readings in a table headed I / A and V / V, plot III against VVV for one length and take the gradient, which equals 1/R1/R1/R, then tabulate R / Ω against length / cm.
- Result: at constant temperature III is proportional to VVV, giving a straight line through the origin; the resistance rises as the wire is made longer and falls when a thicker wire is used.
- Watch out:
- Switch off between readings, because a wire that heats up has a higher resistance and would bend the whole pattern.
- Keep the current small for the same reason, using the variable resistor rather than the battery to control it.
- Press the crocodile clips firmly onto clean wire, since a loose or dirty contact adds a resistance of its own.
- Measure the length between the inside edges of the two clips, not to the ends of the wire, and take at least five different lengths.
- Safety: switch off between readings, because the wire can become hot enough to burn at larger currents.
Working with the resistance equation
- Identify which two of VVV, III and RRR you have been given before choosing which form of the equation to write down.
- Check the units next, because a current given in mA\text{mA}mA has to be converted, so 250 mA250\ \text{mA}250 mA becomes 0.250 A0.250\ \text{A}0.250 A.
- A large resistance paired with a small current is a perfectly normal combination, so do not assume you have gone wrong just because the number looks unusual.
- The p.d. and the current you substitute must belong to the same component, so read the circuit diagram carefully before picking values.
Common Mistake
- Do not swap the meters over: the ammeter goes in series and the voltmeter in parallel, and reversing them changes the circuit completely.
- R=V/IR = V/IR=V/I defines resistance for any component, so it still applies to a filament lamp even though the ratio changes as the lamp heats up.
- Convert milliamps to amps before substituting, or the answer comes out a thousand times too small.
- On a graph of III against VVV the gradient is 1/R1/R1/R, not RRR, so a steeper line means a smaller resistance.
Exam technique
- Describing the experiment earns marks for the ammeter in series, the voltmeter in parallel, and the calculation R=V/IR = V/IR=V/I, so name all three.
- Say that several pairs of readings are taken and averaged, because a method with a single reading rarely gets full marks.
- Mention switching off between readings and keeping the current low, since the temperature precaution is a standard mark on this experiment.
- In a calculation, write the equation, substitute, then give the answer with Ω\OmegaΩ, A\text{A}A or V\text{V}V attached.
Self review
- State the equation for resistance and the unit it is measured in.
- Draw the circuit you would use to measure the resistance of a wire.
- Why should the circuit be switched off between readings?
- A p.d. of 9.0 V9.0\ \text{V}9.0 V drives a current of 0.30 A0.30\ \text{A}0.30 A through a lamp. Calculate its resistance.
- What does the gradient of a graph of III against VVV represent?
