An electric bulb rated 75W is operating on an 240V main supply.Determine the resistance of the heating element
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values.
The power of the electric bulb is $P = 75 \, \text{W}$.
The operating voltage is $V = 240 \, \text{V}$.
Step 2: Use the formula relating power, voltage, and resistance.
The formula for power in terms of voltage and resistance is:
$$P = \frac{V^2}{R}$$
To find the resistance $R$, we can rearrange the formula:
$$R = \frac{V^2}{P}$$
Step 3: Substitute the given values into the formula.
$$R = \frac{(240 \, \text{V})^2}{75 \, \text{W}}$$
Step 4: Calculate the resistance.
$$R = \frac{57600 \, \text{V}^2}{75 \, \text{W}}$$
$$R = 768 \, \Omega$$
The resistance of the heating element is $\boxed{\text{768 } \Omega}$.
