Free Pearson Edexcel International A Level Physics lesson

Charge, energy and circuit conservation

Build circuit equations from what is conserved.

What you’ll learn

  • Distinguish charge flow from energy transfer.
  • Derive series and parallel resistance rules.
  • Select a power equation with the appropriate fixed quantity.

What flows and what is transferred?

Electric current is the rate of flow of charge through a chosen cross-section: I = ΔQ/Δt. Conventional current follows the direction positive charge would move; in a metal, mobile electrons drift in the opposite direction. A cell does not use up charge as it drives a circuit. Charge carriers already exist throughout the conductors, and the circuit response involves an electric field establishing their collective motion.

Potential difference measures energy transferred per unit charge between two points. A component with 4 V across it transfers 4 J for every coulomb passing through, not four coulombs each second. The same current can carry different energy-transfer rates through components with different potential differences. Current is measured with an ammeter in series, while a voltmeter is connected across two points whose energy-per-charge difference is required.

Resistance at an operating point is defined by R = V/I. Ohm’s law is the more restrictive statement that current is proportional to voltage while temperature and other physical conditions remain constant. A hot filament still has a calculable V/I even though it does not have one constant resistance over its entire current–voltage curve. Distinguish a definition from a special behaviour, and state whether resistance refers to a point or an entire linear region.

I = ΔQ/Δt; V = W/Q; R = V/I; 1 A = 1 C s⁻¹ and 1 V = 1 J C⁻¹

Symbols and units

  • I is current in A; ΔQ is charge in C crossing a section during Δt in s.
  • V is potential difference in V; W is transferred energy in J; R is static resistance in Ω.

How the equation explains the idea

  1. Current is charge per time, I = ΔQ/Δt. Potential difference is energy per charge, V = W/Q; these measure different physical quantities.
  2. Combining their units gives VI = (J/C)(C/s) = J/s, a power. Resistance R = V/I describes an operating point; constant R requires the additional ohmic condition.

Worked example

Charge and energy through a sensor

  1. A sensor carries 0.20 A for 30 s, so charge passing is Q = It = 6.0 C.
  2. Its potential difference is 5.0 V.
  3. Energy transferred = VQ = 5.0 × 6.0 = 30 J.

Charge continues through the circuit while energy is transferred to the sensor.

Keep this idea. Current counts charge per time; potential difference measures energy per charge; resistance is their operating-point ratio.

Conservation determines the circuit rules

At a steady junction, total current entering equals total current leaving because charge does not accumulate indefinitely there. Around a complete circuit loop, the total energy supplied per coulomb equals the total transferred away per coulomb. This gives a signed potential-difference balance when each source and component is traversed consistently. A potential rise across a supplying cell and drops across resistors must be assigned signs before adding them.

In a series chain, there is one route, so each component carries the same current I. The total potential difference is V₁ + V₂ = IR₁ + IR₂. Defining an equivalent resistor with V = IReq gives Req = R₁ + R₂. In parallel, both ends of each branch connect to the same two nodes, so each branch has the same voltage V. Adding branch currents V/R₁ and V/R₂ gives 1/Req = 1/R₁ + 1/R₂.

A circuit diagram’s shape does not determine series or parallel connections; node connectivity does. Two components drawn side by side are not necessarily parallel if one endpoint differs. For a mixed network, reduce a recognisable series or parallel part, then restore branch voltages and currents systematically. A parallel equivalent resistance must be smaller than the smallest positive branch resistance, which provides a useful reasonableness check after arithmetic.

ΣIin = ΣIout; Σpotential rises = Σpotential drops; Rseries = ΣR; 1/Rparallel = Σ(1/R)

Symbols and units

  • I is branch current in A; V is potential difference in V; R is resistance in Ω.
  • Σ means the sum over the indicated branches or components.

How the equation explains the idea

  1. Series resistors share current. Their drops sum: V = IR₁ + IR₂ = I(R₁ + R₂), giving Rseries = R₁ + R₂.
  2. Parallel resistors share voltage. Their currents sum: I = V/R₁ + V/R₂, giving 1/Rparallel = 1/R₁ + 1/R₂.
  3. For two equal resistors R, the parallel equivalent is R/2 and the series equivalent is 2R.

Worked example

A parallel pair after a series resistor

  1. A 6 Ω and a 3 Ω resistor in parallel give 1/Req = 1/6 + 1/3 = 1/2, so Req = 2 Ω.
  2. Adding a 4 Ω resistor in series gives total resistance 6 Ω.
  3. An ideal 12 V source supplies 2 A; the parallel pair has 4 V across it.

The branch currents are 4/6 A and 4/3 A, which add back to 2 A.

Keep this idea. Identify nodes, apply charge and energy conservation, then check whether the equivalent resistance is plausible.

Power depends on what the source keeps fixed

Each coulomb passing through a component transfers V joules, and I coulombs pass each second. Multiplying therefore gives power P = VI. For steady voltage and current over time t, energy transferred is W = VIt. Use actual component voltage and current: a supply rating alone does not establish the power in an individual resistor within a larger network.

Substituting V = IR gives P = I²R, while substituting I = V/R gives P = V²/R. Both are algebraically consistent at the same operating point, but they predict different trends when different quantities are held fixed. Increasing R at fixed current raises power, whereas increasing R at fixed voltage lowers it. Do not compare formulas without stating the source conditions that determine I and V.

Electrical input energy can become heating, light, sound or mechanical work. Efficiency is the useful output divided by input, and the useful category depends on the application. A resistor chosen to limit current must also withstand its power dissipation; a resistance value alone is not an adequate specification. For changing current or voltage, use suitable interval sums or a stated average-power model instead of substituting one arbitrary reading into a steady-power formula.

P = VI = I²R = V²/R; W = VIt for steady values; efficiency = useful output/input

Symbols and units

  • P is power in W; V is potential difference in V; I is current in A; R is resistance in Ω.
  • W is energy in J and t is duration in s.

How the equation explains the idea

  1. Energy per charge times charge per second gives P = VI. Substituting V = IR yields I²R; substituting I = V/R yields V²/R.
  2. Doubling R at fixed current doubles power, but doubling R at fixed voltage halves power. Always identify which source quantity is held fixed.
  3. For steady V and I, multiply by time: W = VIt. Use efficiency as a dimensionless ratio of useful to input energy or power.
Fixed voltage and fixed current give opposite trends

Conditions. Two distinct ideal-source experiments on an ohmic resistor: either voltage fixed at 3 V or current fixed at 1 A. The source constraints are alternatives, not simultaneous conditions.

Resistance / Ω; Power / W.

With 3 V fixed, P = 9/R falls as R increases. With 1 A fixed, P = R rises. Both give 3 W at 3 Ω, but this intersection does not make the trends equivalent.

Open the interactive lesson to view the plotted curves and their coordinate tables.

Worked example

A motor’s useful output

  1. A motor draws 0.80 A at 6.0 V, so electrical input power is 4.8 W.
  2. It lifts a 0.20 kg mass at 0.50 m s⁻¹; with g = 10 N kg⁻¹, useful power is mgv = 1.0 W.
  3. Efficiency = 1.0/4.8 = 0.208, or about 21%.

Input power and useful mechanical power measure different energy transfers.

Keep this idea. Choose the power expression after identifying the actual voltage, current and controlled source conditions.

Open the interactive lesson for free practice and reviewed three-question samples when available. New full question sets and timed unit checks are in preparation. Existing complete Physics revision packs retain paid access; existing free teaching PDFs remain free.

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