The Problem:
We are given a single-phase 240V induction watt-hour meter with a meter constant of 500 revolutions per kWh. We need to find the speed of the meter disc when a current of 15A at a power factor of 0.6 lagging is flowing through it.

Understanding the Meter Constant:
The meter constant represents the number of revolutions the meter disc makes for each kilowatt-hour (kWh) of energy passing through it. In this case, the meter disc makes 500 revolutions for every kWh of energy consumed.

Calculating the Energy Consumed:
To determine the energy consumed, we need to calculate the power (in kW) and the time (in hours) for which the current flows.

Calculating the Power:
We are given the current (I) and the power factor (P.F.). We can use the formula:
Power (P) = Voltage (V) * Current (I) * Power Factor (P.F.)
Given:
Voltage (V) = 240V
Current (I) = 15A
Power Factor (P.F.) = 0.6 (lagging)
Using the formula, we can calculate the power:
P = 240 * 15 * 0.6 = 2160W = 2.16kW

Calculating the Time:
To determine the time for which the current flows, we need to convert the energy consumed from kilowatt-hours (kWh) to watts (W). We know that 1 kWh is equal to 1000 W for 1 hour.
Given:
Energy consumed (E) = 1 kWh
Energy consumed in watts (E_watts) = E * 1000 = 1 * 1000 = 1000 W
Now, we can calculate the time (T):
T = Energy consumed (E_watts) / Power (P)
T = 1000 / 2160 hours

Calculating the Speed of the Meter Disc:
We know that the meter disc makes 500 revolutions for every kWh of energy consumed. Therefore, the speed of the meter disc can be calculated by multiplying the number of revolutions per kWh (meter constant) with the energy consumed in kilowatt-hours (E).
Given:
Meter constant = 500 revolutions per kWh
Energy consumed (E) = 1 kWh
Speed of the meter disc = Meter constant * E
Speed of the meter disc = 500 * 1 = 500 revolutions

Converting Revolutions to RPM:
Finally, we need to convert the speed of the meter disc from revolutions to revolutions per minute (rpm). We know that there are 60 minutes in 1 hour.
Given:
Speed of the meter disc (in rpm) = Speed of the meter disc (in revolutions) * 60
Speed of the meter disc (in rpm) = 500 * 60 = 30000 rpm

Correct Answer: 18 rpm

Explanation:
The correct answer is 18 rpm, not 30000 rpm as calculated above. It seems there was an error in the calculations. To determine the correct answer, we need to recalculate the time (T) using the correct power value.

Recalculating the Time:
Using the correct power value,