An energy meter has a constant of 600 rev/kWh. If the meter makes 10 revolutions in 20 s, what is the load in kW? 

Explanation:

Given Problem:

An energy meter has a constant of 600 revolutions per kilowatt-hour (rev/kWh). The meter makes 10 revolutions in 20 seconds. We are tasked to determine the load in kilowatts (kW).

Solution:

The energy meter constant, 600 rev/kWh, indicates that for every kilowatt-hour of energy consumed, the meter's disc completes 600 revolutions. To calculate the load in kilowatts, we need to use the following relationship:

Load (in kW) = (Number of revolutions × Time Conversion Factor) / (Meter Constant × Time in Hours)

Now, let us solve the problem step by step:

Since there are 3600 seconds in an hour, the given time of 20 seconds can be converted to hours as:

Time in hours = 20 seconds ÷ 3600 seconds/hour = 1/180 hours

Load (in kW) = (Number of revolutions × Time Conversion Factor) / (Meter Constant × Time in Hours)

Load (in kW) = (10 revolutions × 1) / (600 rev/kWh × 1/180 hours)

Load (in kW) = (10 × 180) / 600

Load (in kW) = 1800 / 600

Load (in kW) = 3 kW

1. Convert the time from seconds to hours:
2. Substitute the values into the formula:
3. Simplify the equation:

Final Answer: The load is 3 kW.

Important Information:

To evaluate why the other options are incorrect, let's briefly analyze the calculations:

1. Option 1 (0.75 kW): This value would imply a much lower load than calculated. Such a result would occur if either the number of revolutions or the time interval was incorrectly used in the formula.
2. Option 2 (1.5 kW): This value is half the correct answer. This mistake could arise if the time in hours was incorrectly doubled during calculation.
3. Option 4 (6 kW): This value is double the correct answer. Such an error may occur if the number of revolutions was mistakenly doubled or the meter constant was halved.

Conclusion:

The correct solution to the problem is 3 kW, which corresponds to Option 3. This result is consistent with the energy meter's constant, the number of revolutions, and the given time interval. Proper understanding and application of the energy meter formula are essential to solving such problems accurately.