Electric Circuits

Main Content

Power Supplies

Power supplies provide the energy to push current around a circuit. Different types include:

• Cell - A single unit that converts chemical energy into electrical energy. Shown as two parallel lines: one long (positive terminal) and one short/thick (negative terminal).

• Battery - Two or more cells connected together. Shown as multiple cell symbols in a row.

• DC Power Supply - Provides direct current (current flows in one direction only). Shown with + and - signs.

• AC Power Supply - Provides alternating current (current constantly changes direction). Shown with a wavy line (~) symbol.

• Generator - Converts kinetic energy into electrical energy. Shown as a circle with the letter G inside.

Resistors and Variable Components

Resistors are components that resist or slow down the flow of current. They control how much current flows in different parts of a circuit.

• Fixed Resistor - Has a constant resistance value. Shown as a simple rectangle.

• Variable Resistor (Rheostat) - You can change its resistance by moving a slider. This changes the length of wire the current flows through. Shown as a rectangle with a diagonal arrow through it.

• Thermistor (NTC) - A temperature-dependent resistor. NTC means Negative Temperature Coefficient - when temperature increases, resistance decreases. This happens because heating gives atoms more energy to release electrons, so more electrons can flow as current. Shown as a rectangle with a line through it.

• Light-Dependent Resistor (LDR) - Its resistance changes with light intensity. In bright light, resistance is low (more current flows). In darkness, resistance is high (less current flows). Shown as a rectangle inside a circle with two arrows pointing towards it.

Electromagnetic Components

• Magnetising Coil - Creates a magnetic field when current flows through it. Shown as a continuous coiled line.

• Relay - Uses a small current in one circuit to switch on a much larger current in another circuit. Shown as a rectangle with a vertical line through it and a horizontal line across.

• Transformer - Changes (steps up or steps down) voltage and current in AC circuits. Shown as two sets of coils facing each other.

• Fuse - A safety device containing a thin wire that melts if too much current flows, breaking the circuit and preventing damage or fire. Shown as a rectangle with a line passing through the center.

Diodes (Supplement)

Diodes are special components that only allow current to flow in one direction.

• Diode - Shown as a triangle pointing towards a vertical line. Current can only flow in the direction the triangle points. When connected correctly (forward biased), resistance is almost zero and current flows easily. When connected backwards (reverse biased), resistance is extremely high and no current flows.

• Light-Emitting Diode (LED) - Works like a normal diode but emits light when current flows through it. Shown as a diode symbol with two arrows pointing away from it.

Current in Circuits

Current is the flow of electric charge (electrons) around a circuit. It is measured in amperes (A) using an ammeter.

The formula for current is: $I = \frac{q}{t}$

Where:

• I = current in amperes (A)
• q = charge in coulombs (C)
• t = time in seconds (s)

Important: We say current flows from positive to negative (conventional current), but actually electrons flow from negative to positive. For exam purposes, always use conventional current direction (positive to negative).

Current in Series Circuits

A series circuit has only one loop - all components are connected one after another in a line.

Key Rule: In a series circuit, the current is the same at every point. This is because the same number of electrons per second passes through each component.

For example, if you have three ammeters in different positions in a series circuit, they will all show the same reading. If one shows 0.3 A, they all show 0.3 A.

What affects current in series circuits?

1. Voltage of the power supply - If you increase the voltage, more current flows. If you decrease the voltage, less current flows.

2. Number of components - More components means more total resistance, so less current flows. Fewer components means less resistance, so more current flows.

Current in Parallel Circuits

A parallel circuit has multiple loops - components are connected across the same two points, creating separate branches.

Key Rule: In a parallel circuit, current splits at junctions. Some current goes down one branch, and the rest goes down other branches. The current from the power source is larger than the current in any single branch.

At any junction: $I_{total} = I_1 + I_2 + I_3 + ...$

The total current entering a junction equals the total current leaving it. This is because charge cannot be created or destroyed - all the electrons that arrive must leave.

For example, if 4 A enters a junction and splits into two branches, one might carry 2.5 A and the other 1.5 A (2.5 + 1.5 = 4).

Note: Current does not always split equally. More current flows through branches with lower resistance.

Electromotive Force (e.m.f.) and Potential Difference

Electromotive Force (e.m.f.) is the total energy given to each coulomb of charge by the power source (cell or battery). It's measured in volts (V).

Think of e.m.f. as the "pushing power" of a cell - it's the work done per unit charge to move electrons around the complete circuit.

Potential Difference (p.d.) is the energy transferred from electrical energy to other forms (like light or heat) when one coulomb of charge flows between two points. Also measured in volts (V).

Think of p.d. as the "voltage drop" across a component - it's the energy each coulomb loses as it goes through that component.

Cells in Series

When cells are connected in series (positive terminal of one to negative terminal of the next), their e.m.f.s add up:

Examples:

• Two 1.5 V cells in series (both the same way): Total = 1.5 + 1.5 = 3 V
• Three cells: 2 V, 2 V, and 5 V, where the 5 V is opposite: Total = 2 + 2 - 5 = -1 V (which means 1 V in the opposite direction)

Important: If one cell stops working in a series arrangement, the whole circuit turns off.

Potential Difference in Series Circuits (Supplement)

In a series circuit, the total p.d. from the power supply is shared among all the components:

$V_{total} = V_1 + V_2 + V_3 + ...$

Each component gets a share of the voltage. Components with higher resistance get more voltage.

Example: If you have a 16 V battery with a 10 Ω resistor and a 6 Ω resistor in series, and the first resistor has 10 V across it, then the second must have 16 - 10 = 6 V across it.

Potential Difference in Parallel Circuits (Supplement)

In a parallel circuit, each branch gets the full p.d. from the power supply:

$V_1 = V_2 = V_3 = V_{total}$

For example, if you have a 12 V battery connected to two parallel branches, each branch has 12 V across it.

Note: If a branch contains multiple components in series, the 12 V is split between those components.

Resistance in Circuits

Resistance is a measure of how much a component opposes or resists the flow of current. The higher the resistance, the harder it is for current to flow.

Resistance is measured in ohms (Ω).

The formula for resistance is: $R = \frac{V}{I}$

Or rearranged: $V = IR$ (this is Ohm's Law)

Where:

• R = resistance in ohms (Ω)
• V = potential difference in volts (V)
• I = current in amperes (A)

What this means: If a resistor has a resistance of 3 Ω, it needs 3 V to push 1 A of current through it.

Factors Affecting Resistance

The resistance of a wire depends on:

1. Length - Longer wires have more resistance (R ∝ L). Think of it like a longer obstacle course being harder to complete.

2. Cross-sectional area - Thicker wires have less resistance (R ∝ 1/A). More space means electrons can flow more easily.

3. Material - Different materials have different resistivity (ρ). Copper has low resistance; plastic has very high resistance.

4. Temperature - For most conductors, heating increases resistance because atoms vibrate more, getting in the way of electron flow.

The full equation is: $R = \rho \frac{L}{A}$

Where ρ (rho) is resistivity, L is length, and A is cross-sectional area.

Combined Resistance in Series

When resistors are connected in series, the total resistance is the sum of individual resistances:

$R_{total} = R_1 + R_2 + R_3 + ...$

Why? Current has to flow through each resistor one after another, so each one adds to the total opposition.

For identical resistors in series: $R_{total} = n \times R$

Where n is the number of resistors.

Example: Three resistors of 2 Ω, 3 Ω, and 5 Ω in series:

Combined Resistance in Parallel

When resistors are connected in parallel, the total resistance is less than the smallest individual resistance.

Why? Current has multiple paths to flow through, making it easier overall (less total resistance).

For two resistors in parallel (Supplement): $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}$

To find R_total:

1. Calculate 1/R₁ + 1/R₂
2. Take the reciprocal (use the 1/x or x⁻¹ button on your calculator)

For identical resistors in parallel: $R_{total} = \frac{R}{n}$

Example: Two 4 Ω resistors in parallel:

Another example: 50 Ω, 30 Ω, and 100 Ω in parallel: $\frac{1}{R_{total}} = \frac{1}{50} + \frac{1}{30} + \frac{1}{100} = 0.0633$

Ohm's Law and Component Behavior

Ohm's Law states that for some components (at constant temperature), current is directly proportional to voltage: $V \propto I$

Which gives us: $V = IR$

Ohmic conductors are components that obey Ohm's Law. Their resistance stays constant as voltage changes. Example: fixed resistors.

If you plot a graph of voltage (V) against current (I):

• Ohmic conductors give a straight line through the origin
• The steeper the line, the higher the resistance
• The graph closer to the voltage axis has more resistance

Non-ohmic conductors do not obey Ohm's Law. Their resistance changes as voltage changes. Examples: filament lamps, thermistors, diodes.

Special Components: Thermistors and LDRs

Thermistors (NTC)

A thermistor is a temperature-dependent resistor. The NTC type has Negative Temperature Coefficient meaning:

As temperature increases, resistance decreases

Why? Heat gives atoms energy to release more electrons. More free electrons means more current can flow, so resistance decreases.

Uses: Temperature sensors, fire alarms, temperature control circuits

The relationship is:

On a resistance-temperature graph, this gives a decreasing curve.

Light-Dependent Resistors (LDRs)

An LDR is a light-sensitive resistor. Its resistance changes with light intensity:

As light intensity increases, resistance decreases

Uses: Automatic street lights, burglar alarms, light meters

The relationship is:

The Potential Divider Equation

For two resistors R₁ and R₂ in series with voltages V₁ and V₂ across them:

$\frac{R_1}{R_2} = \frac{V_1}{V_2}$

What this means: If one resistor has twice the resistance of another, it gets twice the voltage.

Remember: The total voltage is V₁ + V₂ = total e.m.f.

Example: A circuit has 20 kΩ and 12 kΩ resistors in series. If 5.3 V is across the 12 kΩ resistor, find the total e.m.f.

Using $\frac{R_1}{R_2} = \frac{V_1}{V_2}$: $\frac{12000}{20000} = \frac{5.3}{V_2}$

Total e.m.f. = 5.3 + 8.83 = 14.13 V

Variable Potential Dividers

A variable potential divider uses one fixed resistor and one variable component (rheostat, thermistor, or LDR) in series.

By changing the resistance of the variable component, you change how the voltage is divided.

With a Rheostat:

• Increase rheostat resistance → total resistance increases → current decreases → voltage across rheostat increases, voltage across fixed resistor decreases

With a Thermistor:

• Temperature increases → thermistor resistance decreases → total resistance decreases → current increases → voltage across thermistor decreases, voltage across fixed resistor increases

With an LDR:

• Light intensity decreases → LDR resistance increases → total resistance increases → current decreases → voltage across LDR increases, voltage across fixed resistor decreases

Exam tip: Remember that higher resistance means more voltage across that component (because V = IR, and if current is the same for both, bigger R means bigger V).

This principle is used in:

• Temperature sensors (thermistor potential divider)
• Light sensors (LDR potential divider)
• Volume controls (variable resistor potential divider)

Relationship Between Potential Difference and Resistance (Core)

For a constant current, if resistance increases, the potential difference across that component must increase.

This comes directly from V = IR. If I is constant:

• Double the resistance → double the voltage
• Halve the resistance → halve the voltage

Example: If a component with 10 Ω resistance has 5 V across it with 0.5 A current, and you replace it with a 20 Ω resistor (keeping current at 0.5 A), the voltage becomes:

The voltage doubled because the resistance doubled (current stayed the same).