1. Overview
Resistance is a measure of how much a component opposes the flow of electrical current. Understanding resistance is crucial because it allows engineers to control the amount of current in a circuit, ensuring that electronic devices operate safely and efficiently.
Key Definitions
- Resistance: The ratio of the potential difference across a component to the current flowing through it.
- Ohm ($\Omega$): The unit of electrical resistance.
- Ohmic Conductor: A conductor that follows Ohm’s Law, where current is directly proportional to voltage (at a constant temperature).
- Potential Difference (Voltage): The energy transferred per unit charge between two points in a circuit.
- Current: The rate of flow of electrical charge.
Core Content
The Resistance Equation
To calculate the resistance of a component, we use the following formula: $$Resistance (R) = \frac{Potential Difference (V)}{Current (I)}$$
Worked Example: A light bulb has a potential difference of $12\text{ V}$ across it and a current of $3\text{ A}$ flowing through it. Calculate the resistance.
- $R = V / I$
- $R = 12 / 3$
- $R = 4\text{ }\Omega$
Determining Resistance Experimentally
To find the resistance of an unknown component (e.g., a wire or a resistor), use an ammeter and a voltmeter.
Method:
- Connect the component in series with a power supply and an ammeter.
- Connect a voltmeter in parallel specifically across the component being tested.
- Close the switch and record the reading on the ammeter ($I$) and the voltmeter ($V$).
- (Optional) Use a variable resistor to change the current and take multiple readings to find an average.
- Calculate resistance using $R = V / I$.
Factors Affecting Resistance of a Wire (Qualitative)
The resistance of a metallic wire depends on its physical dimensions:
- Length: The longer the wire, the higher the resistance (electrons collide with more ions).
- Cross-sectional Area (Thickness): The thicker the wire, the lower the resistance (there is more space for electrons to flow).
Extended Content (Extended Curriculum Only)
Current-Voltage ($I-V$) Graphs
The relationship between current and voltage is not the same for all components.
- Fixed Resistor (Ohmic Conductor): At a constant temperature, the graph is a straight line through the origin. Resistance is constant.
- A straight diagonal line passing through (0,0)
- Filament Lamp: As current increases, the temperature of the filament increases, causing resistance to increase. The graph curves, becoming flatter at higher voltages.
- An S-shaped curve passing through the origin
- Diode: A diode only allows current to flow in one direction. It has very high resistance in the reverse direction and low resistance in the forward direction after a certain voltage.
- Horizontal line on the x-axis for negative voltage, then a sharp upward curve for positive voltage
Quantitative Relationships
For a metallic conductor at a constant temperature:
- Resistance is directly proportional to length ($R \propto L$): Doubling the length will double the resistance.
- Resistance is inversely proportional to cross-sectional area ($R \propto 1/A$): Doubling the area will halve the resistance.
Worked Example (Extended): Wire A has a resistance of $10\text{ }\Omega$. Wire B is made of the same metal but is twice as long and has twice the cross-sectional area. What is the resistance of Wire B?
- Length is doubled $\rightarrow$ Resistance doubles ($10 \times 2 = 20\text{ }\Omega$).
- Area is doubled $\rightarrow$ Resistance halves ($20 / 2 = 10\text{ }\Omega$).
- Final Resistance = $10\text{ }\Omega$.
Key Equations
| Equation | Symbols | Units |
|---|---|---|
| $R = \frac{V}{I}$ | $R$ = Resistance, $V$ = Voltage, $I$ = Current | $\Omega$ (Ohms), $V$ (Volts), $A$ (Amps) |
| $R \propto L$ | $L$ = Length | $m$ (Meters) |
| $R \propto \frac{1}{A}$ | $A$ = Cross-sectional area | $m^2$ |
Common Mistakes to Avoid
- ❌ Wrong: Placing the voltmeter in series with the circuit or across the power supply.
- ✅ Right: Always place the voltmeter in parallel across the specific component you are measuring.
- ❌ Wrong: Subtracting current from voltage ($12 - 4$) to find resistance.
- ✅ Right: Always use division ($V / I$).
- ❌ Wrong: Using the symbol for a variable resistor (rectangle with a diagonal arrow) when asked for a fixed resistor.
- ✅ Right: A fixed resistor is a simple plain rectangle.
- ❌ Wrong: Forgetting to convert time units if calculating charge or energy (e.g., leaving 2 minutes as "2").
- ✅ Right: Always convert time to seconds ($2\text{ minutes} = 120\text{ seconds}$).
Exam Tips
- Check Units: Ensure current is in Amps (A), not milliamps (mA). If you see $50\text{ mA}$, divide by $1000$ to get $0.05\text{ A}$ before calculating resistance.
- Identify the Component: If an exam question asks you to identify a component from an $I-V$ graph, look at the shape. A straight line is always a fixed resistor/ohmic conductor; a curve that levels off is a filament lamp.
- Proportionality: If the question says the wire is "thicker" or "wider," it refers to the cross-sectional area. If they give you the diameter or radius, remember that area is proportional to the square of the radius ($A = \pi r^2$).