Electricity

Explanation

• Electric current is the rate of flow of charge, $I=\Delta Q/\Delta t$, measured in amperes. Potential difference is the work done per unit charge, $V=W/Q$, so one volt is one joule per coulomb.
• Resistance is defined as $R=V/I$ and is measured in ohms; this definition remains valid even for a component whose resistance changes with current or temperature.
• Conventional current describes positive charge flow, while electrons in a metal move oppositely.
• In practical circuits an ammeter is connected in series to measure current and a voltmeter in parallel across a component to measure potential difference.
• Examiners expect units, correct meter placement and a distinction between charge transferred, its rate of flow and energy transferred per coulomb.

Explanation

• An ohmic conductor has $I\propto V$ only when physical conditions, especially temperature, remain constant, so its current–voltage characteristic is a straight line through the origin.
• A filament lamp heats as current increases; greater lattice vibration raises its resistance, so an $I$-against-$V$ graph becomes less steep at larger magnitudes.
• A semiconductor diode carries negligible reverse current and little forward current until its turn-on region, after which forward current rises rapidly.
• Either current or potential difference may be placed on the horizontal axis, so gradient meaning must be checked: on an $I$-against-$V$ graph the gradient is conductance.
• Unless stated otherwise, ammeters are ideal with zero resistance and voltmeters are ideal with infinite resistance.

Explanation

• For a uniform wire, resistivity is $\rho=RA/L$, a material property measured in $\Omega\,\text{m}$. Cross-sectional area for a circular wire is $A=\pi d^2/4$, so diameter must be converted to metres before squaring.
• Metal resistance increases with temperature, while the resistance of a negative-temperature-coefficient thermistor decreases; NTC thermistors are temperature sensors whose resistance–temperature graph slopes downward.
• A superconductor has zero resistivity at and below its material-dependent critical temperature, enabling strong magnetic fields and reduced transmission losses.
• Required practical 5 determines wire resistivity using a micrometer, ammeter and voltmeter.
• Examiners expect repeated diameter measurements, a suitable range of lengths or readings, low current to limit heating, and a gradient or repeated calculation with consistent SI units.

Explanation

• Series resistances add, $R_{\text{T}}=R_1+R_2+\cdots$, whereas parallel conductances add, $1/R_{\text{T}}=1/R_1+1/R_2+\cdots$. Conservation of charge means current is the same through series components and currents into a junction equal currents out.
• Conservation of energy means potential rises and drops around a complete loop balance.
• Electrical energy and power follow $E=IVt$ and $P=IV=I^2R=V^2/R$.
• Cells in series have additive emfs; identical cells in parallel retain the emf of one cell and have a smaller effective internal resistance.
• Examiners expect networks to be reduced in a logical order, with branch currents and component potential differences found only after applying the series, parallel, junction and loop relationships.

Explanation

• A potential divider uses series components to provide a constant or variable fraction of a supply potential difference. For two unloaded resistors, the output across $R_2$ is $V_{\text{out}}=V_{\text{in}}R_2/(R_1+R_2)$.
• A variable resistor changes this fraction continuously. Sensor dividers may contain a light-dependent resistor, whose resistance falls as light intensity increases, or an NTC thermistor, whose resistance falls as temperature increases.
• The sensor’s position determines whether output rises or falls with the stimulus: output across a lower sensor falls when its resistance falls.
• The potentiometer as a measuring instrument is not required.
• Examiners expect the output terminals to be identified, the correct resistance placed in the numerator and a circuit designed to achieve the stated response.

Explanation

• Electromotive force is energy supplied by a source per unit charge, $\varepsilon=E/Q$; it is not a mechanical force. A real source has internal resistance $r$.
• When it supplies current $I$ to external resistance $R$, $\varepsilon=I(R+r)$ and terminal potential difference is $V=IR=\varepsilon-Ir$. The term $Ir$ is the lost volts across the internal resistance, so terminal potential difference decreases as current increases.
• On a graph of $V$ against $I$, the intercept is $\varepsilon$ and the gradient is $-r$.
• Required practical 6 finds emf and internal resistance by measuring terminal potential difference over a range of currents.
• Examiners expect a best-fit line, the negative gradient magnitude for $r$, and recognition that terminal potential difference equals emf only when current is zero.