Electric Circuits, Ohm's Law and I-V Characteristics
Electric Current and Charge
Electric current is the flow of charge carriers through a conductor. In metals, these are electrons moving from the negative terminal to the positive terminal — although by convention, current direction is defined as flowing from positive to negative. In solutions (electrolytes), both positive and negative ions carry the current.
Charge is measured in coulombs (C). The equation linking charge, current and time is: \(Q = It\), where \(Q\) is charge in coulombs, \(I\) is current in amperes (A), and \(t\) is time in seconds. One ampere means one coulomb of charge passes a point every second.
Current is measured with an ammeter connected in series with the component. Potential difference (voltage) is measured with a voltmeter connected in parallel.
Potential Difference
Potential difference (p.d.) is the energy transferred per unit of charge that flows between two points. Think of it as the electrical 'push' that drives charge around the circuit. The unit is the volt (V): one volt means one joule of energy is transferred per coulomb of charge.
Resistance and Ohm's Law
Resistance opposes current flow. The relationship between potential difference, current and resistance is given by Ohm's law:
$$V = I \times R$$
Where \(V\) is potential difference in volts, \(I\) is current in amperes, and \(R\) is resistance in ohms (Ω). This can be rearranged: \(I = V/R\) (to find current) and \(R = V/I\) (to find resistance).
An ohmic conductor has a constant resistance at constant temperature. For ohmic conductors, doubling the voltage exactly doubles the current. Most metal resistors behave ohmically at room temperature.
I-V Characteristics
An I-V characteristic graph plots current (y-axis) against potential difference (x-axis). The shape of the graph reveals how resistance behaves. The core practical (Topic 10) requires you to investigate the I-V characteristics of at least a resistor and a filament lamp.
For a fixed resistor at constant temperature, the I-V graph is a straight line through the origin. This confirms that current is directly proportional to potential difference — the definition of an ohmic conductor. The gradient of the line equals \(1/R\): a steeper line means lower resistance.
The same straight-line graph applies for both positive and negative p.d. values — the resistor works the same way in both directions.
The I-V graph for a filament lamp is curved — the gradient decreases as current increases. This is because the tungsten filament heats up as more current flows: higher temperature means more resistance. The graph is symmetrical about the origin (same shape in both directions).
A diode conducts very easily in one direction (forward bias) but has an extremely high resistance in the other direction (reverse bias). Its I-V graph shows almost zero current until the forward voltage threshold is reached, then current rises steeply. In reverse bias, current is essentially zero.
LDRs and Thermistors
Two variable resistors feature prominently in circuit design and exam questions:
A light-dependent resistor (LDR) has a resistance that falls as light intensity increases. In bright conditions, resistance is low; in darkness, resistance is high. LDRs are used in automatic street lighting and camera light meters.
A thermistor (negative temperature coefficient, NTC, type) has a resistance that decreases as temperature increases. They are used in temperature sensors, thermostats, and fire alarms. In a potential-divider circuit, a thermistor can control a relay that switches a heater on or off.
Series and Parallel Circuits
In a series circuit, the same current flows through every component. Voltages add up across components. Total resistance is the sum of individual resistances: \(R_{total} = R_1 + R_2 + R_3\).
In a parallel circuit, each branch has the same potential difference across it (equal to the supply). The total current from the supply equals the sum of the branch currents. Adding more branches decreases the total resistance.
Series: current same everywhere; voltages add up; resistances add up. Parallel: voltage same across all branches; currents add up (junction rule); total resistance is less than the smallest individual resistance. Household appliances are wired in parallel so each receives the full supply voltage.
To plot an I-V characteristic, connect the component in series with an ammeter and a variable resistor (rheostat). Connect a voltmeter in parallel with the component. Adjust the variable resistor to vary the current through the component and record corresponding current and voltage values. Plot I (y-axis) against V (x-axis). Repeat for both polarities where relevant (e.g. a resistor — reverse the cell connections).
For the filament lamp, allow cooling time between readings, as temperature affects resistance. Record at least six evenly spaced values for a reliable graph. Repeat readings to check for anomalies.