A 40W instrument has a resistance 90 Ohms. On what voltage should it be operated normally

Analysis

To solve this problem, we need to relate the power of an electrical instrument to its resistance and the voltage at which it operates. We are given:

• Power ($P$) = 40 W
• Resistance ($R$) = 90 $\Omega$
• Voltage ($V$) = ?

Concept

The relationship between electrical power, voltage, and resistance is given by the formula:

Where:

• $P$ is Power in Watts (W)
• $V$ is Voltage in Volts (V)
• $R$ is Resistance in Ohms ($\Omega$)

Solution

1. Rearrange the formula to solve for $V$: $$V^2 = P \times R$$ $$V = \sqrt{P \times R}$$

2. Substitute the given values into the equation: $$V = \sqrt{40 \times 90}$$

3. Calculate the product: $$40 \times 90 = 3600$$

4. Find the square root: $$V = \sqrt{3600}$$ $$V = 60 \text{ V}$$

Conclusion

The instrument should be operated at 60V. Comparing this result to the provided options, it matches option A.

Exam Tip

When dealing with power formulas, remember the acronym "PIV" ($P=IV$) and "VIR" ($V=IR$). If you combine these, you can derive $P = V^2/R$ or $P = I^2R$ easily without memorizing too many separate formulas. Always check your units before calculating—if the power were in kilowatts (kW), you would need to convert it to Watts (W) first!