B.5.2 Electrical Current and Voltage

Electric Current and Potential Difference

Definition

Electric circuits

Electric circuits are systems where electric charge flows through a closed loop.

To understand how these circuits work, we must first define two fundamental concepts: electric current and electric potential difference.

Electric Current: The Flow of Charge

Definition

Electric current

Electric current is the rate at which electric charge flows through a conductor.

Analogy

Imagine water flowing through a pipe.
The amount of water passing a point per second is similar to the amount of electric charge passing through a wire per second.

Mathematically, current ( $I$ ) is expressed as:

$I = \frac{Δ q}{Δ t}$

where:

$I$ is the current in amperes (A).
$Δ q$ is the change in charge in coulombs (C).
$Δ t$ is the change in time in seconds (s).

Note

The ampere (A) is the unit of electric current, defined as one coulomb of charge passing through a point in a circuit per second.

Direct Current (DC)

In direct current (DC), charge carriers (usually electrons) flow in a single direction.
This is the type of current produced by batteries and used in most electronic devices.

Example

If 6 coulombs of charge pass through a wire in 2 seconds, the current is: $I = \frac{Δ q}{Δ t} = \frac{6 C}{2 s} = 3 A$

Calculating Current

To calculate current, you need to know the total charge passing through a point and the time it takes.

Tip

To find the number of electrons in a given charge, divide the total charge by the charge of a single electron ( $1.6 \times 10^{- 19}$ C).

Example question

Current

A current of 1 A is established in a conductor. How many electrons move through the cross-sectional area of the conductor in 1 s?

Solution

The charge of one electron is $1.6 \times 10^{- 19} C$ .
In 1 second, 1 coulomb of charge passes through the conductor.
The number of electrons is: $\frac{1, C}{1.6 \times 10^{- 19} C / electron} = 6.25 \times 10^{18} electrons$

Electric Potential Difference (Voltage)

Definition

Electric potential difference

Electric potential difference, or voltage, is the energy per unit charge required to move a charge between two points in an electric field.

Mathematically, voltage ( $V$ ) is expressed as:

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

where:

$V$ is the potential difference in volts (V).
$W$ is the work done in joules (J).
$q$ is the charge in coulombs (C).

Note

The volt (V) is the unit of potential difference, defined as one joule of work done per coulomb of charge.

Understanding Voltage

Voltage can be thought of as the "push" that drives charge through a circuit.
It is created by a source of energy, such as a battery, which does work to move charges from a lower potential to a higher potential.

Example question

Potential difference

The work done in moving a charge of $2.0 μ C$ between two points in an electric field is $1.50 \times 10^{- 4} J$ .

Determine the potential difference between the two points.

Solution

Use the formula $V = \frac{W}{q}$ .
Substitute the values: $V = \frac{1.50 \times 10^{- 4} J}{2.0 \times 10^{- 6} C} = 75 V$

Voltage and Energy

Voltage is directly related to the energy transferred to or from a charge.
When a charge moves through a potential difference, it gains or loses energy.

Example question

Speed of the electron

An electron is accelerated from rest through a potential difference of 75 V. What is the speed acquired by the electron?

Solution

The work done on the electron is $W = q V$ , where $q = 1.6 \times 10^{- 19} C$ (the charge of an electron).
The work done is converted into kinetic energy: $W = \frac{1}{2} m v^{2}$
Substitute the values: $1.6 \times 10^{- 19} \times 75 = \frac{1}{2} \times 9.1 \times 10^{- 31} \times v^{2}$
Solve for $v$ : $v = \sqrt{\frac{2 \times 1.2 \times 10^{- 17}}{9.1 \times 10^{- 31}}} = 5.1 \times 10^{6} {ms}^{- 1}$

Connecting Current and Voltage

In a circuit, current and voltage are closely related.

Voltage provides the energy needed to move charges, while current is the flow of those charges.

Analogy

Think of voltage as the pressure in a water pipe and current as the flow of water.
Higher pressure (voltage) pushes more water (charge) through the pipe (circuit).

Calculating Power in a Circuit

Definition

Power in a circuit

The power dissipated in a circuit component is the rate at which energy is transferred.

It can be calculated using the formula:

$P = I V$

where:

$P$ is the power in watts (W).
$I$ is the current in amperes (A).
$V$ is the voltage in volts (V).

Example question

Power dissipated in the resistor

A resistor has a current of 2.0 A flowing through it and a potential difference of 12 V across its ends. What is the power dissipated in the resistor?

Solution

Use the formula $P = I V$ .
Substitute the values: $P = 2.0 A \times 12 V = 24 W$

Key Takeaways

Electric current is the rate of flow of charge, measured in amperes (A).
Electric potential difference (voltage) is the work done per unit charge, measured in volts (V).
Power in a circuit is the product of current and voltage, measured in watts (W).

Self review

How is electric current defined, and what is its unit?
What is the relationship between work, charge, and potential difference?
How would you calculate the power dissipated in a resistor with a current of 3 A and a voltage of 9 V?

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B.5.2 Electrical Current and Voltage

Electric Current and Potential Difference

Electric Current: The Flow of Charge

Direct Current (DC)

Calculating Current

Current

Electric Potential Difference (Voltage)

Understanding Voltage

Potential difference

Voltage and Energy

Speed of the electron

Connecting Current and Voltage

Calculating Power in a Circuit

Power dissipated in the resistor

Key Takeaways

You've read 2/2 free chapters this week.

Electric Circuits