Resistors and Resistance (Copy)
1. Core Concept: What is Resistance?
- Resistance is the opposition to the flow of electric current.
- Greater resistance = smaller current for a given voltage.
Formula:
R = V / I
→ R = resistance (Ω)
→ V = voltage (V)
→ I = current (A)
2. Objectives in ATP Questions
- To measure the resistance of:
- A fixed resistor
- A wire of varying length or thickness
- A lamp or non-ohmic component
- To observe the effect of changing variables (length, material, temperature) on resistance.
- To compare series and parallel resistor combinations
3. Apparatus Required
| Apparatus | Use |
|---|---|
| Power supply (low voltage) | Provides current |
| Ammeter | Measures current (A) – in series |
| Voltmeter | Measures voltage (V) – in parallel |
| Resistor / wire | Component under test |
| Variable resistor (rheostat) | To adjust current safely |
| Metre rule / tape | Measure length of wire |
| Connecting wires | Complete circuit |
4. Method 1: Measuring Resistance of a Fixed Resistor
Step-by-Step:
- Connect resistor in series with ammeter, switch, and power supply.
- Connect voltmeter in parallel across resistor.
- Use variable resistor to adjust current and voltage.
- Record 5–6 sets of readings for V and I.
- Plot a graph of V vs I.
- Calculate R = V / I for each pair, or take gradient of graph.
5. Method 2: Investigating Resistance of a Wire (Varying Length)
Objective: To see how wire length affects resistance
Step-by-Step:
- Use nichrome wire stretched along metre ruler.
- Connect desired length of wire in circuit.
- Keep current low to prevent heating.
- Record voltage across and current through the wire.
- Repeat for several different lengths (e.g. 20 cm, 40 cm… 100 cm).
- Calculate resistance using
R = V / Ifor each length. - Plot a graph:
→ R vs Length (L) → Straight line: resistance ∝ length
6. Sample Data Table (Length vs Resistance)
| Length (cm) | Voltage (V) | Current (A) | Resistance (Ω) |
|---|---|---|---|
| 20 | 0.35 | 0.70 | 0.50 |
| 40 | 0.68 | 0.68 | 1.00 |
| 60 | 1.02 | 0.68 | 1.50 |
| 80 | 1.40 | 0.70 | 2.00 |
7. Graphical Analysis
| Graph | Interpretation |
|---|---|
| V vs I (resistor) | Straight line → constant resistance |
| R vs L (wire) | Straight line through origin → resistance ∝ length |
| I vs V (filament lamp) | Curved → resistance increases with temperature |
✔️ Gradient of V–I graph = resistance
✔️ Linearity = obeys Ohm’s Law
8. Series and Parallel Resistors (ATP-Style Comparison)
| Configuration | Rules | Effect |
|---|---|---|
| Series | R_total = R₁ + R₂ + ... |
Resistance increases |
| Parallel | 1/R_total = 1/R₁ + 1/R₂ + ... |
Resistance decreases |
Practical Verification:
- Measure total current and voltage
- Calculate total R and compare with theoretical
9. Variables and Control
| Type | Example |
|---|---|
| Independent | Length of wire, number of resistors |
| Dependent | Resistance |
| Controlled | Wire material, cross-sectional area, ambient temperature, voltage supply |
10. Common Errors and How to Avoid Them
| Error | Solution |
|---|---|
| Ammeter/voltmeter in wrong position | Ammeter = series, Voltmeter = parallel |
| Parallax reading error | Read meters at eye level |
| Wire heats up, increasing resistance | Keep current low or use short durations |
| Poor connections | Ensure tight, clean connections |
| Varying two variables at once | Change only one variable per trial |
11. Improvement Suggestions
- Use digital meters for precision
- Switch off between readings to avoid heating wires
- Use thicker wires to reduce resistance fluctuations
- Repeat readings and average for reliability
- Ensure length of wire is measured accurately from fixed zero point
12. ATP-Style Questions
| Question Type | Example |
|---|---|
| Method | “Describe how you would measure the resistance of a wire.” |
| Drawing | “Draw a circuit diagram to measure current through and voltage across a resistor.” |
| Graph | “Plot a graph of V vs I and determine resistance.” |
| Calculation | Given V and I, use R = V/I |
| Interpretation | “Explain why the R vs L graph is a straight line through origin.” |
| Error Identification | “Why does resistance increase more than expected?” → Heating |
13. Exam Tips
- Always quote:
→R = V / I
→R_total = R₁ + R₂(series)
→1/R_total = 1/R₁ + 1/R₂(parallel) - Always:
- Label circuit diagram components properly
- Show all working with units (A, V, Ω)
- Use Ohm’s Law only within linear range
- State:
“Repeat and average readings”
“Keep wire material and thickness constant for fair test”