The meter constant of a single phase 240 V induction watt hour meter is 400 revolutions per KWhr. The speed of the meter disc for a current of 10 A of 0.8 pf, lagging will be 

Explanation:

Meter Constant and Speed of Induction Watt Hour Meter

Definition: The meter constant of a watt-hour meter indicates the number of revolutions of the meter's disc for a specific amount of energy consumed, typically expressed in revolutions per kilowatt-hour (rev/kWh). It helps in determining the speed of the disc based on the electrical load connected to the meter.

Problem Statement: In this problem, we are tasked with calculating the speed of the meter's disc for a single-phase 240V induction watt-hour meter with a meter constant of 400 revolutions per kWh. The current is 10A, and the power factor (pf) is 0.8 lagging.

Given Data:

• Meter constant: 400 revolutions per kWh
• Voltage (V): 240 V
• Current (I): 10 A
• Power factor (pf): 0.8 (lagging)

Step-by-Step Solution:

Step 1: Calculate the power consumed (P)

The power consumed in an electrical circuit is given by the formula:

P = V × I × pf

Substituting the given values:

P = 240 × 10 × 0.8

P = 1920 W or 1.92 kW

Step 2: Determine the number of revolutions per second

From the meter constant, we know that the meter completes 400 revolutions for every 1 kWh of energy consumed. To find the revolutions per second, we first calculate the energy consumed per second (in kWh) and then use the meter constant.

Energy consumed per second (in kWh):

The energy consumed per second in kWh is calculated as:

Energy (kWh) = Power (kW) × Time (hours)

For 1 second, time = 1/3600 hours:

Energy = 1.92 × (1/3600)

Energy = 0.000533 kWh

Revolutions per second:

The revolutions per second can be calculated using the meter constant:

Revolutions per second = Energy (kWh) × Meter constant

Revolutions per second = 0.000533 × 400

Revolutions per second = 0.2132 revolutions/second

Step 3: Convert revolutions per second to revolutions per minute (rpm)

To convert revolutions per second to revolutions per minute, multiply by 60:

Revolutions per minute (rpm) = Revolutions per second × 60

Revolutions per minute = 0.2132 × 60

Revolutions per minute = 12.8 rpm

Final Answer:

The speed of the meter disc is 12.8 rpm.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: 16.02 rpm

This option is incorrect. The value of 16.02 rpm is higher than the actual calculation. This might result from incorrectly assuming a higher energy consumption or misinterpreting the meter constant.

Option 3: 18.2 rpm

This option is also incorrect. It overestimates the revolutions per minute, likely due to a similar error in the calculation of power or energy consumed.

Option 4: 21.1 rpm

This option is incorrect as well. It significantly overestimates the speed of the meter disc, which is inconsistent with the given meter constant and load conditions.

Conclusion:

The correct answer is Option 1: 12.8 rpm. This result is derived using the meter constant and the actual power consumed under the given load conditions. Understanding the relationship between power, energy, and the meter constant is crucial for solving such problems accurately.