# Current, Voltage, Resistance & Ohm's Law

This topic is part of the HSC Physics course under the section Electric Circuits.

### HSC Physics Syllabus

• investigate the flow of electric current in metals and apply models to represent current, including:
– I = q/t (ACSPH038)
• investigate quantitatively the current–voltage relationships in ohmic and non-ohmic resistors to explore the usefulness and limitations of Ohm’s Law using:
– W = qV
– V = IR (ACSPH003, ACSPH041, ACSPH043)

### Current, Voltage, Resistance and Ohm's Law Explained

In the study of electricity, three fundamental concepts are essential: current, voltage, and electrical resistance. These are the building blocks for understanding how electric circuits function.

### Electric Current in Metals

Electric current is the flow of electric charge through a material. In metals, this flow is typically due to the movement of free electrons that are ‘loosely’ bound to atoms (delocalised electrons).

The current can be calculated using the formula:

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

where:

• I is the electric current measured in amperes (A) or Coulombs per second (C s–1)
•  is the electric charge measured in Coulombs (C),
• t is the time in seconds (s) over which the charge flows.

For a current to flow, there must be a potential difference (or electric field) present. Recall that positive charges move from higher to lower potential, whereas negative charges move from lower to higher potential. This is because the convention is that potentials are defined with respect to a positive charge.

### Voltage and Electrical Potential Energy

Voltage, or electric potential difference, is the energy per unit charge exerted by an electric field on a charged particle. It is related to the work done to move a charge between two points against the electric field.

Voltage is given by:

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

where:

• W is the work done or energy transferred measured in joules (J),
• q is the charge measured in Coulombs (C),
• V is the voltage measured in volts (V).

When a voltage or potential difference is applied to a conductor, a current is present as the charges e.g. electrons begin to move through the conductor.

Voltage can be thought of as the electric "pressure" that pushes the charges through a conducting material, just like the hydrostatic pressure that is applied to a hose to cause water to flow.

### Conventional Current

While current is defined as the flow of electrons per second, the direction of conventional current is actually defined as the flow of positive charge. This means the direction of conventional current is always opposite to the direction of electron movement.

This convention dates back to the time before electrons were discovered. It was assumed that current flowed from the positive terminal to the negative terminal of a power source. All subsequent physics were then defined relative to this positive to negative flow. As such, when electrons were discovered, scientists believe it was too bothersome to redefine everything in terms of the electron current, thus keeping the conventional current in use.

In electric circuits, conventional current is still used to define the direction of current flow, flowing from a higher electric potential to a lower electric potential. From the standpoint of physics and the actual mechanisms within a circuit, considering electron flow (from lower to higher potential) gives a more accurate depiction of what is physically occurring.

### Ohm’s Law and Electrical Resistance

Ohm's Law is a fundamental principle that describes the relationship between current, voltage, and resistance in an electrical circuit. It states that current passing through a conductor between two points is directly proportional to the voltage across the two points

It is given by:

where:

• V is the voltage,
• I is the current,
• R is the resistance measured in ohms (\Omega).

Electrical resistance is a measure of how much a material opposes the flow of current or movement of charges (electrons).

Several key factors affect electrical resistance:

#### 1. Material

Different materials have different abilities to conduct electric current. This is due to the number of charge carriers (usually electrons) available within the material to carry the current. Materials with more free electrons (like metals) have lower resistance, whereas those with fewer free electrons (like rubber or glass) have higher resistance.

• Conductors: Materials with low resistance, such as copper, aluminum, and silver.
• Insulators: Materials with high resistance, such as rubber, glass, and plastic.
• Semiconductors: Materials with intermediate resistance, such as silicon and germanium.

#### 2. Cross-Sectional Area

The cross-sectional area of a conductor affects its resistance. A wider conductor has a larger area for electrons to flow, reducing resistance.

#### 3. Length

The longer a conductor, the greater its resistance. This is because electrons have to travel a longer distance through the material, and thus there are more chances for collisions with atoms in the material, which impedes their flow.

#### 4. Temperature

Temperature has a significant effect on resistance. For most conductors e.g. metals, as temperature increases, the resistance also increases. This is because the atoms in the conductor vibrate more at higher temperatures, which increases the likelihood of collisions with the charge carriers.

It is important to remember that Ohm's law does not apply to all materials. Materials that obey Ohm's law are known as ohmic resistors, which have a constant resistance and comply with the law regardless of the voltage applied.

For Ohmic resistors, the current is directly proportional to the voltage applied. This is depicted by a linear relationship between current and voltage.

### Non-Ohmic Resistors

Non-ohmic resistors are devices or materials that do not have a constant resistance across different applied voltages, which means their voltage-current graph is not a straight line.

However, in non-ohmic resistors, the equation V = IR may still be used to calculate the third variable given the other two despite 'Ohm’s law not holding'. This is because Ohm’s law does not refer to the the equation, but rather the specific case where resistance is constant, giving direct proportionality. This is a common misconception.

Examples of non-ohmic resistors include:

• Semiconductors: Devices like diodes and transistors, which are based on semiconductor materials, have a non-linear relationship between voltage and current. They are designed to conduct significantly more in one direction than the other, making them key components in digital electronics.

• Thermistors: These are temperature-dependent resistors whose resistance changes significantly with temperature.

• Varistors: These resistors change their resistance with voltage. They are used to protect circuits against voltage spikes by shunting excess current when the voltage exceeds a certain level.

• Light-dependent resistors (LDRs): The resistance of LDRs varies with the intensity of light falling on them. They are used in light-sensitive detector circuits.

### Example 1

A current of 6 amperes is measured in an electric circuit. How much charge passes through a given point in the circuit in 1 minute?

Solution:

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

$$q = (6)(60) = 360 \text{ Coulombs}$$

### Example 2

A 4 A current flows in a wire for 10 minutes. Calculate the total number of electrons passing through a point in this wire during this time.

Solution:

First, calculate the total charge during this time:

$$q = I \times t$$

$$q = (4)(10 \times 60) = 2400 \text{ Coulombs}$$

Since the magnitude of charge of one electron is 1.602 xx 10^{-19},

$$\text{No. of electrons} = \frac{2400}{1.602 \times 10^{-19}} = 1.5 \times 10^{22}$$

### Example 3

An electric circuit is constructed using a 20 V battery and produces a current of 2.5 A. Assume the circuit is an Ohmic resistor.

(a) What is the resistance of the circuit?

(b) If the circuit is reconstructed with a material that gives half the resistance as before, explain what will happen to the voltage and current of this new circuit.

Solution to part (a):

Using Ohm's law:

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

$$R = \frac{20}{2.5} = 8 \, \Omega$$

Solution to part (b):

The voltage applied to the circuit depends on the power source e.g. the battery, and is not affected by the electrical resistance. However, the magnitude of current will be doubled due to Ohm's law. This is because current and resistance are inversely proportional (if voltage is kept constant).