Current, Voltage and Resistance
Charge and Current
Current is the rate at which electric charge flows through a conductor. In metal wires, the charge carriers are free electrons — electrons that are not bound to any particular atom and can drift through the material when a potential difference is applied. For current to flow, two conditions must be met: there must be a potential difference driving the charge, and the circuit must form a complete closed loop with no gaps.
The equation linking charge, current and time is:
$$Q = I \times t$$
Where \(Q\) is charge (coulombs, C), \(I\) is current (amperes, A), and \(t\) is time (seconds, s). One ampere means one coulomb of charge passes a point every second. Current is measured using an ammeter connected in series. Potential difference is measured using a voltmeter connected in parallel across the component.
Current is measured in amperes (A), potential difference in volts (V). Current is NOT ‘used up’ by components — charge flows continuously around a closed circuit. Energy is transferred from the charge carriers, not the current itself.
Resistance and Ohm’s Law
Resistance opposes the flow of current. The greater a component’s resistance, the smaller the current that flows for a given potential difference. The relationship between these three quantities is:
$$V = I \times R$$
Where \(V\) is potential difference (V), \(I\) is current (A), and \(R\) is resistance (\(\Omega\)). This can be rearranged: \(I = \frac{V}{R}\) or \(R = \frac{V}{I}\). Ohm’s Law is a special case of this: it states that the current is directly proportional to the potential difference only if the temperature does not change. Components that obey this are called ohmic conductors.
Question: A resistor has a potential difference of 12 V across it and a current of 0.4 A flowing through it. Calculate its resistance.
Answer: \(R = \frac{V}{I} = \frac{12}{0.4} = 30 \, \Omega\). Note: current in amps, voltage in volts, resistance in ohms. Always write the equation, substitute, then calculate.
I–V Characteristics
An I–V characteristic graph shows how current varies with potential difference. You need to know the shapes for three key components:
• Ohmic resistor: a straight line through the origin. The gradient is constant, showing that resistance does not change. This confirms Ohm’s law.
• Filament lamp: a curve that starts steep and flattens at higher voltages. As more current flows, the filament heats up, increasing its resistance. The curve is symmetrical in both directions.
• Diode: current only flows in the forward direction. In reverse, resistance is extremely high and effectively no current flows. There is a threshold voltage (around 0.6 V for silicon diodes) below which forward current is also negligible.
Ohmic resistor: straight line (constant resistance). Filament lamp: curve (resistance increases with temperature). Diode: current only in one direction (very high reverse resistance).
Series and Parallel Circuits
In a series circuit, all components are in a single loop. The same current flows through every component. Potential difference is shared — the voltages across components add up to the supply voltage. Total resistance is the sum of individual resistances: \(R_{\text{total}} = R_1 + R_2 + R_3\). If any component breaks, the whole circuit stops.
In a parallel circuit, components are on separate branches. Potential difference is the same across every branch (and equal to the supply voltage). Current splits between branches — more current takes the lower-resistance path. Adding resistors in parallel decreases total resistance because there are more paths for charge to flow. If one branch breaks, others continue to work. Household wiring is parallel so that each appliance receives the full 230 V and can be switched independently.
Some components have resistance that responds to environmental conditions:
• A light-dependent resistor (LDR) has high resistance in the dark and low resistance in bright light. It is used in automatic streetlights and security systems.
• An NTC thermistor (negative temperature coefficient) has high resistance when cold and low resistance when hot. It is used in temperature sensors, fire alarms and thermostat circuits.
Both devices are non-ohmic — their resistance changes with conditions, so the current through them is not simply proportional to voltage. They are often used in potential divider circuits to give a variable voltage output.
Series: Two resistors, 6 Ω and 4 Ω, connected in series to a 10 V supply. \(R_{\text{total}} = 6 + 4 = 10 \, \Omega\). \(I = \frac{V}{R} = \frac{10}{10} = 1 \text{ A}\) (same through both).
Parallel (same resistors): Voltage across each branch = 10 V. Current through 6 Ω branch: \(I_1 = \frac{10}{6} \approx 1.67 \text{ A}\). Current through 4 Ω branch: \(I_2 = \frac{10}{4} = 2.5 \text{ A}\). Total current from supply = \(1.67 + 2.5 = 4.17 \text{ A}\) — more than in series, because parallel reduces total resistance.