Ohm's Law is a fundamental principle in the field of electronics and electrical engineering. It states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, with the proportionality constant being the resistance (R) of the conductor. The formula for Ohm's Law is:
\[ V = I \cdot R \]
To find the resistance, we can rearrange the formula to solve for \( R \):
\[ R = \dfrac{V}{I} \]
Where:
- \( V \) is the voltage (measured in volts, V)
- \( I \) is the current (measured in amperes, A)
- \( R \) is the resistance (measured in ohms, \(\Omega\))
Example 1: Resistance in a Household Circuit
Question: A household circuit has a voltage of 120 volts across a light bulb and a current of 3 amperes flowing through it. What is the resistance of the light bulb?
Calculation:
Given:
- \( V = 120 \) V
- \( I = 3 \) A
Using the formula:
\[ R = \dfrac{V}{I} = \dfrac{120}{3} = 40 \, \Omega \]
Result: The resistance of the light bulb is 40 ohms.
Example 2: Resistance in a Car Headlight
Question: A car headlight has a voltage of 12 volts across it and a current of 2 amperes flowing through it. What is the resistance of the headlight?
Calculation:
Given:
- \( V = 12 \) V
- \( I = 2 \) A
Using the formula:
\[ R = \dfrac{V}{I} = \dfrac{12}{2} = 6 \, \Omega \]
Result: The resistance of the car headlight is 6 ohms.
Example 3: Resistance in a Smartphone Charger
Question: A smartphone charger has a voltage of 5.04 volts across it and a current of 1.2 amperes flowing through it. What is the resistance of the charger?
Calculation:
Given:
- \( V = 5.04 \) V
- \( I = 1.2 \) A
Using the formula:
\[ R = \dfrac{V}{I} = \dfrac{5.04}{1.2} = 4.2 \, \Omega \]
Result: The resistance of the smartphone charger is 4.2 ohms.
By understanding and applying Ohm's Law, we can easily calculate the resistance in various devices and circuits. This is essential for designing and troubleshooting electrical and electronic systems.
