4.2.4 Resistance

This section focuses on understanding and applying the concept of resistance in electrical circuits. We will review the relationship between voltage, current, and resistance, and the formula that connects them.

Understanding Resistance

Resistance is the opposition to the flow of electric current. Materials with high resistance impede the flow of current, while materials with low resistance allow current to flow easily. Resistance is measured in Ohms (╬®).

The Ohm's Law Equation

The fundamental relationship between voltage (V), current (I), and resistance (R) is described by Ohm's Law:

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

Where:

• R = Resistance (measured in Ohms, ╬®)
• V = Voltage (measured in Volts, V)
• I = Current (measured in Amperes, A)

This equation states that the resistance of a conductor is directly proportional to the voltage applied across it and inversely proportional to the current flowing through it.

Using the Equation

To use this equation effectively, you need to know two of the values (V, I, or R) and then calculate the third.

Example 1: Calculating Resistance

A resistor has a voltage of 12V applied across it and a current of 0.5A flowing through it. Calculate the resistance of the resistor.

Using the formula: $$R = \frac{V}{I}$$

Substituting the values: $$R = \frac{12V}{0.5A}$$

$$R = 24 \Omega$$

Therefore, the resistance of the resistor is 24 Ohms.

Example 2: Calculating Current

A circuit has a resistance of 10╬® and a voltage of 5V. Calculate the current flowing through the circuit.

Using the formula: $$R = \frac{V}{I}$$

Rearranging the formula to solve for I: $$I = \frac{V}{R}$$

Substituting the values: $$I = \frac{5V}{10\Omega}$$

$$I = 0.5A$$

Therefore, the current flowing through the circuit is 0.5 Amperes.

Example 3: Calculating Voltage

A component has a resistance of 20╬® and a current of 2A flowing through it. Calculate the voltage across the component.

Using the formula: $$R = \frac{V}{I}$$

Rearranging the formula to solve for V: $$V = IR$$

Substituting the values: $$V = 2A \times 20\Omega$$

$$V = 40V$$

Therefore, the voltage across the component is 40 Volts.

Table Summary

Quantity	Symbol	Unit
Resistance	R	Ohm (╬®)
Voltage	V	Volt (V)
Current	I	Ampere (A)

Understanding and applying Ohm's Law is crucial for analyzing and designing electrical circuits.