Energy Meter Operation Details

This solution explains how to calculate the meter constant for a single-phase energy meter based on its operating conditions and performance. The meter constant, typically expressed in revolutions per kilowatt-hour (rev/kWh), indicates how many times the meter's disc rotates to measure one unit of energy.

Electrical Parameters for Calculation

To determine the energy meter constant, we need to consider the electrical parameters provided:

• Supply Voltage ($V$): 230 V
• Load Current ($I$): 20 A
• Power Factor ($\cos \phi$): 1 (Unity Power Factor - UPF)
• Time Duration ($t$): 2 hours
• Observed Revolutions ($N$): 1380 revolutions

Meter Constant Calculation Steps

The calculation involves determining the total energy consumed and then relating it to the number of revolutions the meter disc made.

1. Calculate Real Power (P):

   The real power consumed by the load is calculated using the formula for a single-phase circuit:

   $$ P = V \times I \times \cos \phi $$

   Substituting the given values:

   $$ P = 230 \, \text{V} \times 20 \, \text{A} \times 1 $$

   $$ P = 4600 \, \text{W} $$

2. Convert Power to Kilowatts (kW):

   Energy is measured in kilowatt-hours (kWh), so we convert the power from Watts (W) to kilowatts (kW):

   $$ P_{\text{kW}} = \frac{P_{\text{W}}}{1000} $$

   $$ P_{\text{kW}} = \frac{4600 \, \text{W}}{1000} $$

   $$ P_{\text{kW}} = 4.6 \, \text{kW} $$

3. Calculate Energy Consumed (E):

   The total energy consumed over the specified time duration is calculated as:

   $$ E = P_{\text{kW}} \times t $$

   Using the calculated power and the given time:

   $$ E = 4.6 \, \text{kW} \times 2 \, \text{h} $$

   $$ E = 9.2 \, \text{kWh} $$

4. Calculate Meter Constant (K):

   The meter constant ($K$) is defined as the ratio of the number of revolutions to the energy consumed in kWh:

   $$ K = \frac{\text{Total Revolutions}}{\text{Energy Consumed}} $$

   $$ K = \frac{N}{E} $$

   Plugging in the values:

   $$ K = \frac{1380 \, \text{rev}}{9.2 \, \text{kWh}} $$

   To simplify the division:

   $$ K = \frac{13800}{92} \, \text{rev/kWh} $$

   $$ K = 150 \, \text{rev/kWh} $$

Calculated Meter Constant Result

Based on the calculations, the meter constant for the single-phase energy meter under the given load conditions is 150 rev/kWh.