9702 · 9.3
Resistance and resistivity flashcards
Revision flashcards for Cambridge 9702 Resistance and resistivity (syllabus 9.3). Flip, recall, then mark a real past-paper question.
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What is the formula for resistance in terms of potential difference and current?
Resistance ($R$) is defined as the ratio of potential difference ($V$) across a component to the current ($I$) flowing through it: $R = V/I$.
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How does the resistance of a metal conductor change with increasing temperature, and why?
It increases. Higher temperatures cause metal atoms to vibrate more, leading to more frequent collisions with charge carriers (electrons), impeding their flow.
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Define resistivity ($ ho$) and state its formula.
Resistivity ($ ho$) is an intrinsic material property that quantifies its inherent ability to resist charge flow, independent of its physical dimensions. Formula: $\rho = \frac{RA}{L}$.
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Describe the resistance behaviour of a thermistor and an LDR.
A thermistor's resistance *decreases* as temperature *increases*. An LDR's resistance *decreases* as light intensity *increases*.
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What is a superconductor, and what is a key application?
A superconductor is a material that exhibits zero electrical resistivity when cooled below a specific critical temperature. A key application is in powerful electromagnets (e.g., for MRI scanners or maglev trains).
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What is Ohm's Law and for which type of conductor does it apply?
Ohm's Law states that for an **ohmic conductor**, current is directly proportional to potential difference, provided its temperature remains constant.
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How does a filament lamp demonstrate non-ohmic behaviour?
Its resistance increases as the current (and thus temperature) rises. This is due to increased atomic vibrations impeding electron flow, making its I-V graph non-linear.
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What is the key difference in resistance behaviour between an ideal ammeter and an ideal voltmeter?
An ideal ammeter has **zero resistance** to not affect the circuit current, while an ideal voltmeter has **infinite resistance** to prevent current from flowing through it, ensuring accurate voltage measurement.
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Explain why semiconductor diodes are considered non-ohmic components.
Their resistance is not constant; it's very low in forward bias (above a threshold voltage) and extremely high in reverse bias, leading to a non-linear I-V graph.
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What are the units for resistance and resistivity?
The unit for resistance ($R$) is the Ohm ($\Omega$). The unit for resistivity ($\rho$) is the Ohm-metre ($\Omega$m).
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Sketch the I-V graph for a filament lamp. How does resistance change along the curve?
The graph is a curve that starts at the origin and bends towards the voltage axis. As voltage (and current) increases, the gradient (I/V) decreases, meaning resistance (V/I) increases. This is due to the filament heating up.
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Sketch the I-V graph for a semiconductor diode.
The graph shows almost zero current in reverse bias (negative V). In forward bias (positive V), current is negligible until a threshold voltage (≈0.7V for silicon), after which it increases exponentially. This shows very high resistance in reverse and low resistance in forward bias.
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How does the cross-sectional area of a wire affect its resistance?
Resistance is inversely proportional to the cross-sectional area ($R \propto 1/A$). A thicker wire (larger A) has lower resistance because there are more pathways for the charge carriers to flow.
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Why does the resistance of an NTC thermistor decrease as temperature increases?
In a semiconductor like a thermistor, increasing temperature provides energy to release more charge carriers (electrons and holes) from the atomic lattice, increasing the number density of charge carriers ($n$). This effect outweighs the increased lattice vibrations, leading to a decrease in resistance.