Current of electricity

01

Current, charge and electron flow

Current tells you how quickly charge passes a point in a circuit. A larger current means more charge passes each second.

Charge is measured in coulombs, C. Electrons carry negative charge. In a metal wire, mobile electrons can drift through the material while the positive ions remain in its structure.

Electric current is the rate of flow of charge. It is measured in amperes, A. One ampere means one coulomb passes a cross-section each second: 1 A = 1 C/s. Equivalently, 1 C = 1 A s: a coulomb is an ampere-second. Current is represented by I; charge by Q or q.

Imagine marking one cross-section of a wire and counting the total charge that passes it during an interval. A steady 0.30 A means 0.30 C passes each second. It does not mean the whole wire contains only 0.30 C of charge.

Conventional current and electron drift

Conventional current is defined in the direction in which positive charge would move. In the external circuit of a discharging cell, it goes from the positive terminal, through the components, towards the negative terminal.

Electrons are negative, so their drift in the metal wire is in the opposite direction: from the negative terminal towards the positive terminal through the external circuit. The cell symbol's long line marks its positive terminal and its short line the negative terminal.

A lamp transfers energy as charge passes through it; it does not use up that charge. Electrons are already present throughout the metal circuit. Do not picture the lamp waiting for one electron to leave the cell and complete a whole journey before it responds.

Q = It applies directly when I is constant over the interval. For a changing current, use the average current for that interval, or find the charge in each stated constant-current part and add the amounts. An instantaneous reading does not establish the current throughout a long interval.

Measure current through a component

An ammeter, shown as a circle containing A, connects in series with the branch being measured. Open the circuit at the chosen position and include the meter in the path, so the branch's charge passes through it.

For a d.c. measurement, connect its positive terminal on the side from which conventional current enters. Choose a suitable range; if the expected value is uncertain, start with a sufficiently high range and reduce it when appropriate for a clearer reading. Keep the reading within the selected range.

An ammeter has very low resistance. Connecting it directly across a cell would provide a low-resistance path, rather than measure the current through the intended component. The resistance arrangement shows the correct current and voltage connections together.

An ammeter reads amperes, not coulombs. To determine charge for a steady current, also measure the time interval, for example with a stopwatch, then use Q = It.

02

E.m.f. and potential difference

Voltage describes energy transferred per coulomb of charge. The source and the component have different roles in that energy transfer.

Work done is an energy transfer, measured in joules, J. Charge is measured in coulombs, C. Current measures coulombs per second; voltage measures joules per coulomb.

Electromotive force: e.m.f.

The e.m.f. of a source is the work done per unit charge by the source in driving charge around a complete circuit. It is measured in volts. A 1.5 V source supplies 1.5 J per coulomb in this energy account.

Potential difference: p.d.

The p.d. across a component is the work done per unit charge in driving charge through the component. It is measured in volts. A p.d. of 3.0 V means 3.0 J is transferred in that component for each coulomb passing through it.

Small voltages may be given in millivolts: 1 mV = 0.001 V. Divide a reading in millivolts by 1000 to convert it to volts.

A cell transfers energy from its chemical store into the electrical pathway. In a resistor, energy is transferred to internal stores; in a motor, part can be transferred mechanically to a load. Charge carries on through the circuit while energy is transferred. The energy stores and pathways account helps keep these two ideas separate.

The name electromotive force does not mean a force measured in newtons. E.m.f. is an energy-per-charge quantity, just as p.d. is. Neither quantity measures how many coulombs pass each second.

Measure voltage across two points

A voltmeter, shown as a circle containing V, connects in parallel across the component: one lead at each of its terminals. This measures the p.d. between those two points. It is not inserted into the main current path as an ammeter is.

For a positive d.c. reading, connect the meter's positive lead to the higher-potential side and its negative lead to the lower-potential side. Reversing the leads reverses the sign shown by a suitable digital meter; it does not mean the component has changed its resistance.

Select a voltage range that includes the expected reading. For example, a 0-5 V range is unsuitable for a 6.0 V p.d. Once a suitable range is established, finer resolution helps distinguish nearby readings. For an analogue scale, read at eye level to reduce parallax.

A voltmeter connected across a source with no other external circuit can give an estimate of its e.m.f. when the meter draws negligible current. For the ideal-source model, the source's terminal p.d. equals its e.m.f. The combined meter diagram instead measures the p.d. across a resistor.

03

Resistance and wire dimensions

Resistance relates the potential difference across a component to the current through it. At the same p.d., a greater resistance gives a smaller current.

Current I is measured through a component in amperes. Potential difference V is measured across its terminals in volts. Use readings for the same component when finding its resistance.

This defines resistance at the stated operating point: the voltage and current under the conditions of that reading. It does not by itself establish that a component's resistance stays the same when conditions change.

How wire dimensions affect resistance

Compare wires of the same material at the same temperature. Changing the material or temperature can change the relationship between their dimensions and resistance.

Greater length gives greater resistance

Resistance is proportional to length, R ∝ L. Doubling the length while keeping the cross-section unchanged doubles the resistance. Charge must travel through a longer section of the material.

Greater cross-sectional area gives smaller resistance

Resistance is inversely proportional to cross-sectional area, R ∝ 1/A. Doubling that area while keeping length unchanged halves the resistance. The wider cross-section provides more conducting material alongside the path.

The cross-sectional area is the area you see when looking straight at a cut end. It is not the curved outer surface of the wire. For a circular wire, A = πd²/4, so area changes with the square of the diameter.

Determine resistance and investigate wire length

Use a suitable low-voltage classroom supply, with an ammeter in the current path and a voltmeter across the component. Record the p.d. and current together after the readings settle, and calculate R = V/I. Check meter ranges and polarity before collecting readings.

To investigate length, use the same uniform wire and vary the distance between its electrical contacts. Measure this active length with a ruler. The unused wire beyond the contacts is not part of the measured section.

1. Keep the wire's material and cross-sectional area fixed. Use several measured active lengths.
2. At each length, record the current through and p.d. across that section. Calculate its resistance from the paired readings.
3. Keep the wire temperature as steady as practical: use a suitably low current and switch off between readings where appropriate. Wait for it to return to the comparison conditions if it warms.
4. Plot resistance vertically against active length horizontally. Proportionality predicts a straight line through the origin for the wire alone at constant cross-section and temperature.

If diameter is needed, use a micrometer or suitable calipers, check for zero error and take readings at several positions and orientations. Avoid squeezing or measuring a damaged part of the wire. Convert the diameter to consistent units before calculating area.

Contact and lead resistance may add to a measured resistance, depending on the voltage lead positions. Wire heating can change readings, and a varying diameter means the cross-section is not uniform. Repeating and averaging readings can reveal scatter, but it does not automatically remove these effects. Explain the specific limitation and how the method addresses it.

Twice the diameter is four times the area. Also keep the voltage and current paired: dividing a voltage across one branch by the current through a different branch does not generally give either branch's resistance.

04

Temperature and I-V characteristics

An I-V graph shows how a component's current responds to different potential differences. Its shape tells you whether the resistance stays constant.

At any nonzero-current operating point, R = V/I. Read both values from that same point. The graphs here put current I in amperes on the vertical axis and p.d. V in volts on the horizontal axis.

Why a hotter metal has greater resistance

When a metallic conductor's temperature rises, the ions in its structure vibrate more vigorously. Their increased vibration hinders the drift of mobile electrons, so the resistance increases in the normal operating range considered here.

At the same p.d., the hotter conductor therefore carries a smaller current. This explanation concerns metals; it is not a rule that every material or component has increasing resistance with temperature.

Read and sketch three characteristic shapes

Start with labelled axes and an origin. Positive and negative values represent opposite voltage polarities and current directions under a fixed reference convention.

Metallic conductor at constant temperature

Sketch a straight line through the origin, extending into both positive and negative quadrants. Current is proportional to p.d., so V/I is constant. This is an ohmic conductor under those conditions. A wire that heats significantly is no longer being compared at constant temperature.

Filament lamp

Sketch a curve through the origin that becomes less steep as the voltage magnitude increases, with a corresponding branch for reversed polarity. Greater current heats the metal filament, increasing its resistance. Doubling the p.d. therefore need not double the current.

Semiconductor diode

Identify the forward and reverse polarities. In the forward direction, current rises strongly over the illustrated higher-voltage part of the curve. In reverse, it is negligible over the range shown. Sketch this asymmetric behaviour; there is no single exact turn-on voltage for every diode.

The diode's forward and reverse directions describe its orientation in the circuit. They are not a claim that all positive voltages in every drawing are forward: check the stated reference and component orientation. The displayed small reverse-current range does not establish zero current at every possible reverse voltage.

Calculate resistance at a point

For the straight I-V line through the origin, the gradient is I/V = 1/R. Here 0.30/6.0 = 0.050 A/V, whose reciprocal is 20 Ω. A steeper straight line on the same scales means smaller resistance.

For a curved graph, use the point's V/I. A tangent gradient describes how current changes close to that point; its reciprocal is not the resistance V/I there. Likewise, a ratio of changes between two separated points does not generally give either point's resistance. If the axes are exchanged to V vertically and I horizontally, the constant-resistance line instead has gradient R.

Collect readings that can distinguish the behaviours

Measure current through and p.d. across the component while varying a suitable low-voltage supply. Record paired readings, then plot I against V. For the constant-temperature wire comparison, limit heating and allow the wire to return to the same conditions between readings where needed.

For a lamp characteristic, let each reading settle at its operating condition; the changing filament temperature is part of the behaviour being observed. Use suitable component ratings and current limits. To investigate the opposite polarity, switch off before reversing the source connections and record the resulting signs consistently.

State the graph's axes and conditions. A straight line through the origin supports constant resistance over the range shown. A changing gradient on a lamp curve must be interpreted with the filament's changing temperature.