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A-Level Circuit symbols and diagrams, resistance and resistivity, series and parallel resistors, and RC circuits
What the A-Level syllabus expects for Circuit symbols and diagrams, resistance and resistivity, series and parallel resistors, and RC circuits, and how to practise it.
What the syllabus expects
- Know and deploy the standard circuit symbols
- Sketch and read circuit diagrams assembled from switches and sources, both fixed and variable resistors, capacitors, diodes, lamps, voltmeters, ammeters, thermistors, light-dependent resistors, and whatever other parts the syllabus mentions
- Define a component's resistance as the voltage across it over the current through it, and apply V = IR
- Use R = ρl/A, which links a conductor's resistance to its resistivity, its length and its cross-sectional area, in problems
- Draw and read the I–V curves of d.c. components: a filament lamp, an NTC thermistor, a semiconductor diode and an ohmic resistor
- Account for how resistivity shifts with temperature in ordinary metals such as a filament lamp and in semiconductors such as an NTC thermistor, invoking carrier drift velocity and carrier number density respectively
- Understand how a source's internal resistance drags down both its terminal voltage and its output power
- Work out how several resistors wired in series add up to one overall resistance, and use that in problems
- Work out how several resistors wired in parallel reduce to one overall resistance, and use that in problems
- Handle networks mixing series and parallel resistors on a single e.m.f. source, potential dividers included, some of which carry NTC thermistors or light-dependent resistors
- Apply the formulas for the combined capacitance of capacitors joined in series and in parallel
- Portray how current, charge and voltage evolve over time as a capacitor charges or discharges through a resistor, using x = x0 e^(−t/τ) or x = x0[1 − e^(−t/τ)]
Scope: τ = RC is the time constant
How it's examined
About 7% of the past-paper style questions in Rae's bank for this subject sit in this topic.
Worked examples
Example 1 (4 marks)
(a)(iii) Using the potential differences around the circuit, demonstrate that the total charge Q stored on the capacitor network after a time t is described by: Q = Q0 (1 − e^(−t / (R C_eq))) in which Q0 represents the greatest charge the capacitor network can hold. [4]
Show the worked answer
Apply Kirchhoff's voltage law round the charging loop. The EMF E equals the p.d. across R plus the p.d. across the capacitor network: E = iR + Q/C_eq, with i = dQ/dt. So E = R dQ/dt + Q/C_eq. At t -> infinity the current is zero and the charge is maximum Q0, giving E = Q0/C_eq. Substitute: Q0/C_eq = R dQ/dt + Q/C_eq => R dQ/dt = (Q0 - Q)/C_eq => dQ/(Q0 - Q) = dt/(R C_eq). Integrate from Q=0 at t=0 to Q at t: -ln(Q0 - Q) + ln(Q0) = t/(R C_eq) => ln[Q0/(Q0 - Q)] = t/(R C_eq) => Q0 - Q = Q0 e^(-t/(R C_eq)) => Q = Q0 (1 - e^(-t/(R C_eq))). (shown)
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