Resistance
Section: Electricity & Magnetism | Syllabus: Cambridge IGCSE Physics (0625)
What is Resistance?
- The resistance of a conductor is the opposition it offers to the flow of electric current
- a good conductor has low resistance; a poor conductor has high resistance
- Formula:
- R = (V/I)
- Where:
- R = resistance (Ω)
- V = p.d. (V)
- I = current (A)
- Unit:
- resistance is measured in ohms (Ω)
- a conductor has a resistance of 1 Ω if a p.d. of 1 V causes a current of 1 A to flow (1 Ω = 1 V/A)
Worked Example: Calculating Resistance
Museli has a resistor with a current of 2 A flowing through it when the p.d. across it is 10 V, and wants to find its resistance.
- Step 1: write down the equation. R = (V/I)
- Step 2: substitute the values. R = (10/2)
- Step 3: calculate the answer. R = 5 Ω
Measuring Resistance
Resistance can be found experimentally using a voltmeter and an ammeter.
- Set up a circuit with the resistor, an ammeter connected in series, and a voltmeter connected in parallel across the resistor
- Record the current I from the ammeter and the p.d. V from the voltmeter
- Calculate the resistance: R = V/I
The ammeter reads I and the voltmeter reads V, so resistance R = V/I
Factors Affecting the Resistance of a Wire
- For a metallic wire, resistance depends on its length, cross-sectional area, material and temperature
- a longer wire has a higher resistance
- a thicker wire (larger cross-sectional area) has a lower resistance
- different materials have different resistivities
- for metals, a higher temperature gives a higher resistance
Quantitative Relationships
Extended Only
- Resistance is directly proportional to length:
- R ∝ L
- double the length → double the resistance
- Resistance is inversely proportional to cross-sectional area:
- R ∝ (1/A)
- double the cross-sectional area → halve the resistance
Worked Example: Effect of Length on Resistance
Muumbe has a wire of length 50 cm with a resistance of 4 Ω, and wants to find the resistance of a similar wire of length 150 cm.
- Step 1: since R ∝ L, write the ratio. (R_2/R_1) = (L_2/L_1)
- Step 2: substitute the values. R_2 = 4 × (150/50)
- Step 3: calculate the answer. R_2 = 12 Ω
Current-Voltage (I-V) Graphs
Extended Only
Fixed Resistor (Ohmic Conductor)
A straight line through the origin means constant resistance
- Straight line through the origin
- Current is directly proportional to p.d.
- Resistance is constant at constant temperature
Filament Lamp
The curve flattens as the filament heats up and its resistance increases
- Curve through the origin
- As current increases, the filament heats up and its resistance increases
- The gradient decreases at higher currents
Diode
A diode only conducts once the forward voltage passes the threshold
- Current flows in one direction only (forward bias)
- Very high resistance in the reverse direction - effectively no current flows
- Low resistance once the forward voltage exceeds a threshold (about 0.6 V for silicon)
Interactive revision notes, videos and practice questions load below.