Ohm's Law

Ohm's Law states that at constant temperature and other physical factors, the potential difference across the ends of a conductor is directly proportional to the current passing through the conductor (wire).

The mathematical expression of Ohm's Law is:

$V = I \times R$

Where:

• V is the potential difference (voltage) across the conductor in volts (V).
• I is the current flowing through the conductor in amperes (A).
• R is the resistance of the conductor in ohms (Ω).

Example: Suppose a conductor has a resistance of $R = 10\ \Omega$ and the current flowing through it is $I = 2\ \text{A}$. What is the potential difference across the conductor?

Step 1: Use Ohm's Law: $V = I \times R$

Step 2: Substitute the given values into the formula:

$V = 2\ \text{A} \times 10\ \Omega$

Step 3: Multiply:

$V = 20\ \text{V}$

Final Answer: The potential difference across the conductor is $V = 20\ \text{V}$.

Graphical representation of Ohm's Law

1. If we plot voltage (V) on the y-axis and current (I) on the x-axis, the graph will show a straight line passing through the origin (0, 0).

   

2. The gradient (slope) of this line represents the resistance of the conductor.

3. The resistance of a given conductor is constant if the temperature and other physical factors remain unchanged.

4. Doubling the voltage will result in doubling the current, as the relationship is directly proportional.

Factors that affect the resistance of a conductor

The resistance of a conductor is influenced by the following factors:

Length of the conductor

1. The resistance of a conductor is directly proportional to its length.
2. Longer wires have higher resistance because the electrons collide more often as they travel through the wire.
3. Shorter wires offer less resistance because there's less distance for the electrons to travel.

Temperature

1. Resistance generally increases with temperature.
2. As temperature rises, atoms in the conductor vibrate more, making it harder for electrons to pass through.
3. Metals like copper experience an increase in resistance as their temperature increases. This phenomenon is used in temperature sensors like resistance thermometers, which measure changes in resistance with temperature.

Types of material

1. Different materials have different resistivities, which determine how well they conduct electricity.
2. Conductors like copper and silver have low resistivity and, therefore, low resistance, making them ideal for electrical wiring.
3. Insulating materials like rubber or plastic have very high resistivity, meaning they resist the flow of electricity and are used for coating wires.
4. For example, copper has lower resistance compared to chrome for the same dimensions, which is why copper is widely used for electrical conductors.

Cross-sectional area

1. The resistance of a conductor is inversely proportional to its cross-sectional area.
2. A thicker wire (larger cross-sectional area) has lower resistance because it provides more paths for the electrons to flow through, reducing collisions.
3. A thinner wire (smaller cross-sectional area) has higher resistance because there are fewer paths for current to flow.
4. For instance, the filament of a light bulb is made from a thin wire with high resistance. This high resistance causes the filament to heat up and emit light.

SI units of current, voltage, and resistance

Current (I): The rate of flow of electric charge through a conductor.

• SI Unit: Ampere (A)
• Measured using: Ammeter

Voltage (V): The potential difference across two points in a circuit, which drives the current.

• SI Unit: Volt (V)
• Measured using: Voltmeter

Resistance (R): The opposition to the flow of electric current in a conductor.

• SI Unit: Ohm (Ω)
• Calculated using the formula:

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

Where:

• V is the voltage in volts (V).
• I is the current in amperes (A).
• R is the resistance in ohms (Ω).