Single-Phase Induction-Type Energy Meter Calculation

Given Information:
- Constant speed of 1300 revolutions/kWh
- 150 W load rotates the disc at 4.2 rpm
- Load is on for 11 hours

Calculations:

- Number of revolutions made by the disc in 11 hours:
- 4.2 rpm x 60 mins x 60 secs x 11 hours = 1663200 revolutions
- Energy consumed by the load in kWh:
- Energy (kWh) = Power (kW) x Time (hours)
- Energy (kWh) = 150 W / 1000 x 11 hours
- Energy (kWh) = 1.65 kWh
- Number of revolutions expected for the energy consumed:
- Expected revolutions = Energy consumed x Constant speed
- Expected revolutions = 1.65 kWh x 1300 revolutions/kWh
- Expected revolutions = 2145 revolutions
- Error in the meter reading:
- Error = Actual revolutions - Expected revolutions
- Error = 1663200 revolutions - 2145 revolutions
- Error = 1661055 revolutions

Percentage Error:

- Percentage error in the meter reading:
- Percentage error = (Actual reading - Expected reading) / Expected reading x 100
- Percentage error = (1661055 - 2145) / 2145 x 100
- Percentage error = 77445.2%

Explanation:

- Single-phase induction-type energy meters work on the principle of electromagnetic induction. The meter uses a rotating disc which is driven by a magnetic field produced by the current flowing through the load.
- The speed of the disc is directly proportional to the power consumed by the load. The constant speed of the disc is measured in revolutions per kilowatt-hour (kWh).
- In this problem, the load consumes 1.65 kWh of energy in 11 hours. The number of revolutions made by the disc is calculated using the constant speed of 1300 revolutions/kWh.
- The expected number of revolutions for the energy consumed is 2145 revolutions. However, the actual number of revolutions made by the disc is 1663200 revolutions. This means that the meter has recorded an error of 1661055 revolutions.
- The percentage error in the meter reading is calculated using the formula (Actual reading - Expected reading) / Expected reading x 100. The percentage error in this case is 77445.2%, which is a very large error.
- This error could be due to various reasons such as mechanical wear and tear of the meter, incorrect calibration, etc. It is important to periodically test and calibrate the energy meter to ensure accurate readings.