A-Level Physics: Electricity and Circuits Revision Guide

Electricity forms one of the most mathematical and practical topics in A-Level Physics, connecting microscopic electron behaviour to everyday circuits and power systems. Success requires both conceptual understanding of what current, voltage, and resistance actually represent, and fluency with circuit calculations and analysis. Whilst some students find electricity abstract compared to mechanics, the systematic approaches and clear rules make it highly approachable once you grasp the fundamentals.

Current, Charge, and the Nature of Electricity

Electric current represents the flow of charge through a conductor. Current I is defined as charge Q flowing past a point per unit time: I = Q/t. One ampere equals one coulomb per second. Current flows from positive to negative terminal in conventional current (the historical convention), though electrons actually flow the opposite direction since they’re negatively charged. For most A-Level purposes, conventional current is what matters.

In metal conductors, charge carriers are free electrons—outer electrons not bound to specific atoms. When a voltage is applied, these electrons drift slowly through the conductor at typical speeds around 0.1 mm/s, though individual electrons move much faster in random directions. This drift velocity might seem incredibly slow, but circuits respond almost instantly because the electric field propagates through the conductor at near light speed, causing electrons throughout the conductor to start drifting essentially simultaneously.

Charge is quantised in units of the elementary charge e = 1.6 × 10^(-19) C, the magnitude of an electron’s charge. Current is the collective motion of enormous numbers of these charge carriers—one ampere means about 6.25 × 10^18 electrons passing a point each second. This quantisation isn’t usually relevant for circuit calculations but becomes important for understanding semiconductor devices.

Voltage, Energy, and Potential Difference

Voltage or potential difference V between two points represents the energy transferred per unit charge moving between those points: V = W/Q where W is energy in joules and Q is charge in coulombs. One volt means one joule per coulomb. Voltage is what drives current through circuits—higher voltage provides more energy per charge, driving more current through a given resistance.

Electromotive force (emf) is the total voltage supplied by a source like a battery or cell when no current flows—the maximum potential difference the source can provide. When current flows, some voltage is “lost” inside the source due to internal resistance, so the terminal voltage (voltage actually available to the external circuit) is less than the emf.

Power—the rate of energy transfer—relates to current and voltage through P = IV. This fundamental relationship allows calculation of power in any circuit component if you know current through it and voltage across it. Alternative forms derived from Ohm’s law give P = I²R (power dissipated in resistance R carrying current I) and P = V²/R (power dissipated across resistance R with voltage V across it). All three forms are useful in different contexts.

Resistance and Ohm’s Law

Resistance R measures how much a component opposes current flow. Ohm’s law—arguably the most important relationship in circuit theory—states V = IR for ohmic conductors. Higher resistance means less current for a given voltage, or equivalently, more voltage needed to drive a given current. Resistance is measured in ohms (Ω), where one ohm means one volt produces one ampere.

Not all components obey Ohm’s law. Ohmic conductors like metal wires have constant resistance independent of current or voltage—plotting voltage against current gives a straight line through the origin. Non-ohmic components like filament bulbs have resistance that changes with current (the filament heats up, increasing resistance as current increases). Semiconductor diodes conduct readily in one direction but barely at all in the reverse direction, producing highly non-linear I-V characteristics.

Temperature affects resistance significantly for most materials. Metal conductors have resistance that increases with temperature as atomic vibrations impede electron flow. Thermistors are semiconductors designed to have resistance that changes dramatically with temperature—NTC (negative temperature coefficient) thermistors decrease resistance as temperature rises, PTC (positive temperature coefficient) thermistors increase resistance with temperature. These make useful temperature sensors.

Resistivity ρ is a material property that determines resistance, whilst resistance depends on both material and geometry. For a wire of length L, cross-sectional area A, and resistivity ρ, resistance R = ρL/A. Longer wires have more resistance (electrons must travel further), thicker wires have less resistance (more space for parallel current paths). Copper’s low resistivity (about 1.7 × 10^(-8) Ωm) makes it excellent for wiring.

Series and Parallel Circuits

Series components connect end-to-end so the same current flows through all of them. The key relationships for series circuits are: current is the same everywhere (I_total = I₁ = I₂ = I₃), total voltage equals the sum of individual voltages (V_total = V₁ + V₂ + V₃), and total resistance equals the sum of individual resistances (R_total = R₁ + R₂ + R₃). Adding more resistors in series increases total resistance because current must pass through each resistor in turn.

Parallel components connect across the same two points so voltage across each component is the same. The key relationships are: voltage is the same across all components (V_total = V₁ = V₂ = V₃), total current equals the sum of individual currents (I_total = I₁ + I₂ + I₃), and reciprocals of resistances add to give reciprocal of total resistance (1/R_total = 1/R₁ + 1/R₂ + 1/R₃). Adding more resistors in parallel decreases total resistance because current can flow through multiple paths simultaneously.

For two resistors in parallel, a useful shortcut is R_total = (R₁ × R₂)/(R₁ + R₂)—product over sum. For equal resistances R in parallel, total resistance is R/n where n is the number of resistors. Three 60Ω resistors in parallel give total resistance 60/3 = 20Ω.

Most real circuits combine series and parallel elements. Systematic analysis is essential: identify sections that are in series or parallel with each other, simplify those sections, then analyse the resulting simpler circuit. Work systematically from the most deeply nested parallel or series combinations outward until you’ve simplified to a single equivalent resistance.

Kirchhoff’s Laws and Circuit Analysis

Kirchhoff’s first law (current law or junction rule) states that total current entering a junction equals total current leaving it. This reflects charge conservation—charge doesn’t accumulate at junctions. At a junction where 5A enters via one wire and leaves via two other wires, those two currents must sum to 5A.

Kirchhoff’s second law (voltage law or loop rule) states that the sum of voltages around any closed loop in a circuit equals zero. This reflects energy conservation—a charge gaining energy from a battery must lose that same energy going through resistors and other components. Going around a loop, count voltages as positive when going from negative to positive terminal of a source, negative when going through resistors in the direction of current flow.

These laws enable analysis of complex circuits that aren’t simple series-parallel combinations. Define currents in each branch (guessing directions if necessary—wrong guesses just give negative values), write down current equations for each junction, and voltage equations for independent loops, then solve the simultaneous equations. This systematic approach always works though it can involve messy algebra.

Internal Resistance and Real Sources

Real batteries and power supplies have internal resistance r that limits the current they can supply. When current flows, voltage is “lost” inside the source, so terminal voltage V = ε - Ir where ε is the emf and I is the current. The terminal voltage decreases as current increases—batteries can’t maintain their full voltage under heavy load.

Maximum power is delivered to an external load when the load resistance equals the internal resistance. This “impedance matching” is important in audio systems and power transfer applications, though it means only 50% efficiency (half the power is wasted in the internal resistance). For maximum efficiency, you want load resistance much larger than internal resistance, though this delivers less total power.

Short-circuiting a battery (connecting terminals directly with negligible resistance) causes current I = ε/r limited only by internal resistance. This can be very large, causing dangerous overheating. Internal resistance provides some protection against short-circuit damage, though it’s still not safe to short-circuit batteries deliberately.

Potential Divider Circuits

Potential dividers use two resistors in series to produce a lower voltage from a source. For resistors R₁ and R₂ in series across voltage V_in, the voltage across R₂ is V_out = V_in × R₂/(R₁ + R₂). The larger resistor gets more voltage proportionally—twice the resistance means twice the voltage.

Variable potential dividers use a potentiometer (variable resistor with a sliding contact) to provide continuously adjustable voltage output. Moving the slider changes the ratio R₁:R₂, varying the output voltage from zero to V_in. This simple circuit enables volume controls, brightness adjustments, and sensor interfaces.

Potential dividers with sensors (LDR, thermistor, strain gauge) produce voltages that vary with the sensed quantity. An LDR (light-dependent resistor) in a potential divider produces voltage that changes with light level, enabling automatic light controls. A thermistor in a potential divider produces temperature-dependent voltage for temperature monitoring. These simple circuits are fundamental to sensor applications.

Loading effects occur when you connect something to a potential divider’s output. The load draws current, acting as a third resistor in parallel with R₂, which changes the voltage division. To minimise loading, the load resistance should be much larger than R₂. Buffers (high input impedance amplifiers) can isolate potential dividers from their loads.

Electrical Power and Heating Effects

When current flows through resistance, electrical energy converts to thermal energy at rate P = I²R. This Joule heating is responsible for electric heating elements, but also for unwanted energy loss in cables and components. Power loss in transmission cables explains why electricity is transmitted at very high voltage—for given power, higher voltage means lower current, and since losses go as I²R, losses are dramatically reduced at high voltage.

Fuses and circuit breakers protect circuits from excessive current that would cause dangerous overheating. A fuse contains a wire that melts at a specific current, breaking the circuit. If a fault causes excessive current, the fuse melts before cables overheat and cause fire. Choose fuse ratings slightly above normal operating current but well below the current that would damage equipment or wiring.

Energy calculations use E = Pt or E = VIt or E = I²Rt depending on what information is available. For a 2kW kettle operating for 3 minutes, E = Pt = 2000 × 180 = 360,000 J = 360 kJ. Electricity bills measure energy in kilowatt-hours: 1 kWh = 3.6 MJ, the energy supplied by 1 kW for 1 hour.

UpGrades provides systematic practice with electricity calculations and circuit analysis, building your confidence with problem-solving approaches and developing fluency with the relationships between current, voltage, resistance, and power that underpin all circuit work.