Current Electricity Fundamentals

Overview

Current electricity studies the movement of electric charge in conducting paths and the transfer of energy in electrical circuits. It forms the foundation for later study of circuit networks, sensing devices, and alternating-current systems.

This chapter focuses on:

• electric charge and current
• current direction conventions
• potential difference and emf
• resistance and Ohm’s law
• non-ohmic behaviour (overview)
• resistivity (overview)
• internal resistance (overview)
• electrical power and energy transfer
• simple resistance combinations

For deeper treatment, see:

• I-V Characteristics
• Internal Resistance
• Resistivity and Materials
• Electrical Power and Ratings
• Current Electricity Common Exam Traps

Core Ideas

• current electricity links charge transport with energy transfer
• conventional current direction is opposite to electron flow in metals
• potential difference and emf are both energy-per-charge ideas, but they describe different roles
• current, voltage, resistance, and power are handled as scalars in H2 circuit analysis
• real sources and non-ohmic devices require more than just $V=IR$

Exam Relevance

This topic is the foundation for later circuit analysis. Most errors come from confusing emf with terminal p.d., mixing current direction conventions, using Ohm’s law too broadly, or choosing the wrong power relation.

Charge and Current

Electric Charge

Charge is a property of matter responsible for electrical effects.

SI unit:

• coulomb (C)

Elementary charge:

$$e=1.60\times 10^{-19}\text{C}$$

Electric Current

Electric current is the rate of flow of charge.

$$I=\frac{\Delta Q}{\Delta t}$$

Where:

• $I$ = current (A)
• $\Delta Q$ = charge passing a point
• $\Delta t$ = time taken

For steady current:

$$Q=It$$

Scalar or Vector?

In H2 circuit analysis:

• current is usually treated as a signed scalar quantity
• sign indicates chosen direction relative to circuit convention

Although charge carriers move with direction, circuit equations usually do not require full vector treatment.

Conventional Current vs Electron Flow

Conventional Current

Defined as the direction positive charge would move.

In circuit diagrams:

• current flows from higher potential to lower potential externally

Electron Flow in Metals

Electrons are negatively charged, so in metallic wires they drift opposite to conventional current.

Conventional current direction is opposite to electron flow in metals.

Potential Difference

Potential difference between two points is:

energy transferred per unit charge.

$$V=\frac{W}{Q}$$

Where:

• $V$ = potential difference (V)
• $W$ = energy transferred (J)
• $Q$ = charge (C)

Meaning:

$$1\text{ V}=1{\text{ J C}}^{-1}$$

Potential difference is a scalar quantity.

Electromotive Force (emf)

The emf of a source is:

energy supplied per unit charge by the source.

$$\mathcal{E}=\frac{W}{Q}$$

Examples:

• cells
• batteries
• generators

emf is also a scalar quantity.

emf vs Potential Difference

Quantity	Meaning
$\mathcal{E}$	Energy supplied per unit charge by source
$V$	Energy transferred per unit charge between two points

A battery may have emf $\mathcal{E}$ but terminal p.d. can be lower when current flows.

See Internal Resistance.

Resistance

Resistance measures opposition to current flow.

$$R=\frac{V}{I}$$

Unit:

$$\Omega$$

Resistance is treated as a scalar quantity.

Ohm’s Law

For an ohmic conductor at constant temperature:

$$V=IR$$

So:

• current is proportional to voltage
• resistance remains constant

Non-Ohmic Behaviour (Overview)

Some components do not obey a constant $V/I$ ratio.

Examples:

• filament lamp
• diode
• thermistor
• LDR

Their resistance changes with temperature, light level, or applied voltage.

See I-V Characteristics.

Resistivity (Overview)

Resistance depends on material and dimensions.

$$R=\rho \frac{l}{A}$$

Where:

• $\rho$ = resistivity
• $l$ = length
• $A$ = cross-sectional area

Interpretation:

• longer wire → larger resistance
• thicker wire → smaller resistance
• different materials have different resistivity

See Resistivity and Materials.

Internal Resistance (Overview)

Real sources are not ideal. They may contain internal resistance $r$.

If current $I$ flows:

$$\mathcal{E}=V+Ir$$

Hence:

$$V=\mathcal{E}-Ir$$

Where:

• $V$ = terminal potential difference
• $Ir$ = lost volts inside source

See Internal Resistance.

Electrical Power and Energy Transfer

Power

Rate of electrical energy transfer:

$$P=IV$$

Alternative forms:

$$P=I^{2}R$$ $$P=\frac{V^2}{R}$$

Energy Transferred

$$W=Pt$$

So:

$$W=VIt$$

See Electrical Power and Ratings and Work, Energy and Power.

Basic Resistance Combinations

Series

• same current through each component
• voltages add

$$R_{\text{total}}=R_1+R_2+\cdots$$

Parallel

• same voltage across each branch
• currents add

$$\frac{1}{R_{\text{total}}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots$$

More detail belongs in DC Circuits.

Short Worked Examples

Example 1: Charge Flow

A current of $2.0\text{ A}$ flows for $5.0\text{ s}$.

$$Q=It=(2.0)(5.0)=10\text{ C}$$

Example 2: Resistance

A resistor has $V=12\text{ V}$ and $I=3.0\text{ A}$.

$$R=\frac{V}{I}=\frac{12}{3.0}=4.0\Omega$$

Example 3: Power

A heater draws $5.0\text{ A}$ from a $240\text{ V}$ supply.

$$P=IV=(240)(5.0)=1200\text{ W}$$

How to Choose Formulas Quickly

If charge and time known:

$$I=\frac{Q}{t}$$

If voltage and current known:

$$R=\frac{V}{I}$$

If resistor heating:

$$P=I^{2}R$$

If fixed voltage across resistor:

$$P=\frac{V^2}{R}$$

If source has internal resistance:

$$V=\mathcal{E}-Ir$$

Common Exam Pitfalls

1. Confusing emf with terminal p.d.

They are not always equal.

2. Reversing electron flow and current direction

Electrons move opposite to conventional current in metals.

3. Using Ohm’s law for non-ohmic devices blindly

Lamp, diode, thermistor may not have constant resistance.

4. Wrong power formula choice

Use the formula matching known quantities.

5. Forgetting units

• A = ampere
• V = volt
• $\Omega$ = ohm
• W = watt
• J = joule

For a compact revision warning sheet, see:

Current Electricity Common Exam Traps

Formula Summary

Quantity	Formula
Current	$I=\frac{\Delta Q}{\Delta t}$
Charge	$Q=It$
Potential difference	$V=\frac{W}{Q}$
Resistance	$R=\frac{V}{I}$
Ohm’s law	$V=IR$
Resistivity	$R=\rho \frac{l}{A}$
Power	$P=IV$
Power	$P=I^{2}R$
Power	$P=\frac{V^2}{R}$
Energy	$W=Pt=VIt$
Internal resistance	$\mathcal{E}=V+Ir$

Related Links

• I-V Characteristics
• Internal Resistance
• Resistivity and Materials
• Electrical Power and Ratings
• Current Electricity Common Exam Traps
• DC Circuits
• Work, Energy and Power
• Potential Divider
• Potentiometer
• Thermistors and LDRs

Links

• Related concept: I-V Characteristics
• Related concept: Internal Resistance
• Related concept: Resistivity and Materials
• Related concept: Electrical Power and Ratings
• Related concept: Current Electricity Common Exam Traps
• Related topic: DC Circuits