Resistance
Section: Electricity | Syllabus: Cambridge AS Level Physics 9702
Resistance Resistance is defined as the ratio of the potential difference across a component to the current flowing through it. Resistance R = fraction where R = resistance (Ω), V = potential difference (V), I = current (A) Resistance is measured in ohms (Ω) .
One ohm is the resistance when a p.d. of one volt causes a current of one ampere. Unit Relationship 1 Ω = 1 V A^-1 (one volt per ampere) Rearranging gives the familiar form: V = IR and I = fraction Worked Example: Basic Resistance Calculation Question: A lamp passes a current of 500 mA when a p.d.
of 3.0 V is applied. Calculate its resistance. Solution Convert current: I = 500 mA = 0.50 A R = fraction = fraction = 6.0 Ω Ohm's Law Ohm's law states that for a conductor at constant temperature, the current through it is directly proportional to the potential difference across it.
Ohm's Law For a metallic conductor at constant temperature: V I This means fraction = constant, i.e., resistance is constant. Important Distinction The equation V = IR is the definition of resistance and applies to all components.
Ohm's law is the statement that resistance is constant (only true for ohmic conductors under constant physical conditions). Components that obey Ohm's law are called ohmic conductors . Their I–V graph is a straight line through the origin.
I–V Characteristics An I–V characteristic is a graph showing how current varies with potential difference for a component. The shape reveals whether the component is ohmic or non-ohmic. 1. Metallic Conductor at Constant Temperature (Ohmic) FIG 9.7: I-V Characteristic for an Ohmic Resistor Show a straight line through the origin with I on the vertical axis and V on the horizontal axis.
The line extends into both positive and negative quadrants, demonstrating constant gradient (constant resistance). Graph shape: Straight line through the origin Current is directly proportional to p.d.
Resistance is constant (gradient is constant) Obeys Ohm's law Finding Resistance from Graph For an ohmic conductor, R = fraction at any point, OR R = fraction of the I–V graph (since gradient = fraction = fraction).
2. Filament Lamp (Non-Ohmic) FIG 9.8: I-V Characteristic for a Filament Lamp Show a curve through the origin that is steep near the origin and becomes progressively less steep (flatter) at higher values of V and I.
The curve is symmetric in both positive and negative quadrants. Graph shape: Curve that starts steep and becomes less steep at higher currents Near the origin (low currents), the graph is approximately linear As current increases, the graph curves - the same increase in V produces a smaller increase in I Resistance increases as current increases Explanation: FIG 9.9: Filament Lamp Heating Effect Show two side-by-side views of a lamp filament: (1) At low temperature - metal ions in a lattice with small vibrations, electrons pass relatively easily.
(2) At high temperature - ions vibrate with larger amplitude, causing more frequent collisions with electrons and increased resistance. Higher current causes more heating of the filament Increased temperature causes metal ions to vibrate more Electrons collide more frequently with vibrating ions This impedes electron flow, increasing resistance Common Misconception Resistance at a point is NOT the gradient of the tangent - it is the ratio fraction at that point (equivalent to the gradient of a line from the origin to that point).
3. Semiconductor Diode FIG 9.10: I-V Characteristic for a Semiconductor Diode Show an asymmetric curve with virtually no current for negative V (reverse bias region). For positive V, show a sharp exponential increase in current once V exceeds approximately 0.7 V (forward bias threshold for silicon).
Graph shape: Asymmetric - conducts in one direction only Forward bias (positive p.d.): Very low resistance once threshold voltage (~0.7 V for silicon) is exceeded; current increases rapidly Reverse bias (negative p.d.): Extremely high resistance; essentially no current flows A diode only allows significant current in one direction, making it useful for rectification.
Resistivity Resistivity is a property of a material that indicates how strongly it opposes current flow. Unlike resistance, resistivity does not depend on the size or shape of the sample. Resistivity R = fraction where R = resistance (Ω), ρ = resistivity (Ω m), L = length (m), A = cross-sectional area (m^2) Rearranging: ρ = fraction Understanding the Relationship FIG 9.11: Effect of Length and Cross-Sectional Area on Resistance Show two comparisons: (1) Two wires of the same cross-sectional area but lengths L and 2L - doubling length doubles resistance.
(2) Two wires of the same length but cross-sectional areas A and 2A - doubling area halves resistance. Resistance is proportional to length : R L (longer wire = more collisions = higher resistance) Resistance is inversely proportional to area : R fraction (thicker wire = more paths for electrons = lower resistance) Units of Resistivity Fr…
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