Resistance
Section: Electricity & Magnetism | Syllabus: Cambridge AS Level Physics 9702
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. Resistance The ratio of potential difference across a conductor to the current flowing through it.
R = V/I Where: R = resistance (Ω), V = p.d. (V), I = current (A) The Ohm The unit of resistance is the ohm (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 Measuring Resistance Resistance can be measured using a voltmeter and ammeter: Set up circuit with resistor, ammeter (in series), voltmeter (in parallel across resistor) Record the current I and p.d.
V Calculate resistance: R = V/I FIG 4.2.23: Circuit for measuring resistance Circuit diagram showing: battery connected to ammeter (A) in series with a resistor (R). A voltmeter (V) is connected in parallel across the resistor.
Ammeter measures current I through the resistor; voltmeter measures p.d. V across it. R = V/I. Factors Affecting Resistance of a Wire For a metallic wire, resistance depends on: Factor Effect on Resistance Relationship Length (L) Longer wire → higher resistance R L (directly proportional) Cross-sectional area (A) Thicker wire → lower resistance R 1/A (inversely proportional) Material Different materials have different resistivities - Temperature Higher temp → higher resistance (for metals) - Summary Double the length → double the resistance Double the cross-sectional area → halve the resistance Current-Voltage (I-V) Graphs 1.
Ohmic Conductor (Fixed Resistor) FIG 4.2.24a: I-V graph for ohmic conductor Graph with current I on y-axis and voltage V on x-axis. A straight line passes through the origin with constant positive gradient.
The line extends into both positive and negative quadrants (symmetric through origin). Straight line through origin. Current is directly proportional to p.d. Resistance is constant at constant temperature.
2. Filament Lamp FIG 4.2.24b: I-V graph for filament lamp Graph with current I on y-axis and voltage V on x-axis. Curve passes through origin. At low V, curve is steep (low resistance when cold). At higher V, curve flattens (gradient decreases as filament heats up and resistance increases).
S-shaped curve symmetric through origin. Curve through origin. As current increases, filament heats up, resistance increases . Gradient decreases at higher currents. 3. Diode FIG 4.2.24c: I-V graph for diode Graph with current I on y-axis and voltage V on x-axis.
For negative V (reverse bias): line flat along x-axis (no current). For positive V: no current until threshold voltage (~0.6V), then current rises steeply (exponential curve upward). Current flows only in one direction (forward bias).
Very high resistance in reverse direction. Low resistance once forward voltage exceeds threshold (~0.6V for silicon). Worked Examples Example 1: Calculating Resistance Question: A current of 2 A flows through a resistor when the p.d.
across it is 10 V. Calculate its resistance. Answer R = V/I = 10/2 = 5 Ω Example 2: Effect of Length Question: A wire of length 50 cm has resistance 4 Ω. What is the resistance of a similar wire of length 150 cm?
Answer Since R L: R_2/R_1 = L_2/L_1 R_2 = R_1 × L_2/L_1 = 4 × 150/50 = 12 Ω
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