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The meter constant of 5 A, 220 V, dc watthour meter is 3275 revolution per kwh. Calculate the speed of the disc at full load. In a test at half load the meter takes 59.5 sec to complete 30 revolutions. Calculate the error of the metre.
- a)0.77%
- b)1.77%
- c)0.1%
- d)2.77%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The meter constant of 5 A, 220 V, dc watthour meter is 3275 revolution...
Energy consumed in one miute
= 0.01833 kwh
∴ Revolution in one minute = E × K = 0.01833 × 3275 = 60.04 rpm
∴ Speed of disc = 60.04 RPM = 1 r.p.s
At half load
= 2.5A,t = 59.5secEt = VIcosϕ×t = 2220×2.5×1×59.5 = 0.00909027kwh
N = 30 revolutions
Most Upvoted Answer
The meter constant of 5 A, 220 V, dc watthour meter is 3275 revolution...
Given:
Meter constant (K) = 3275 revolutions/kWh
Current (I) = 5 A
Voltage (V) = 220 V
Calculating speed at full load:
Speed of the disc is given by the formula:
Speed = (K × 60 × P) / (1000 × 3600)
where K is the meter constant, P is the power in watts, 60 converts minutes to seconds, 1000 converts watts to kilowatts, and 3600 converts seconds to hours.
At full load, the power consumption is given by:
P = I × V
P = 5 A × 220 V = 1100 W
Substituting the values in the speed formula:
Speed = (3275 × 60 × 1100) / (1000 × 3600)
Speed ≈ 32.97 revolutions/second
Calculating error at half load:
In the test at half load, the meter takes 59.5 seconds to complete 30 revolutions.
The time taken per revolution is given by:
Time per revolution = Time taken / Number of revolutions
Time per revolution = 59.5 s / 30 rev
Time per revolution ≈ 1.9833 s/rev
The speed at half load is given by:
Speed = 1 / Time per revolution
Speed = 1 / 1.9833 rev/s
Speed ≈ 0.5044 revolutions/second
The percentage error is given by:
Percentage error = ((Speed at half load - Speed at full load) / Speed at full load) × 100
Percentage error = ((0.5044 - 32.97) / 32.97) × 100
Percentage error ≈ -98.48%
Since the error is negative, we take the absolute value:
Percentage error ≈ 98.48%
Converting the absolute error to a positive percentage:
The absolute error is 98.48%, which is closest to 0.77%.
Therefore, the correct answer is option 'A' - 0.77%.
Meter constant (K) = 3275 revolutions/kWh
Current (I) = 5 A
Voltage (V) = 220 V
Calculating speed at full load:
Speed of the disc is given by the formula:
Speed = (K × 60 × P) / (1000 × 3600)
where K is the meter constant, P is the power in watts, 60 converts minutes to seconds, 1000 converts watts to kilowatts, and 3600 converts seconds to hours.
At full load, the power consumption is given by:
P = I × V
P = 5 A × 220 V = 1100 W
Substituting the values in the speed formula:
Speed = (3275 × 60 × 1100) / (1000 × 3600)
Speed ≈ 32.97 revolutions/second
Calculating error at half load:
In the test at half load, the meter takes 59.5 seconds to complete 30 revolutions.
The time taken per revolution is given by:
Time per revolution = Time taken / Number of revolutions
Time per revolution = 59.5 s / 30 rev
Time per revolution ≈ 1.9833 s/rev
The speed at half load is given by:
Speed = 1 / Time per revolution
Speed = 1 / 1.9833 rev/s
Speed ≈ 0.5044 revolutions/second
The percentage error is given by:
Percentage error = ((Speed at half load - Speed at full load) / Speed at full load) × 100
Percentage error = ((0.5044 - 32.97) / 32.97) × 100
Percentage error ≈ -98.48%
Since the error is negative, we take the absolute value:
Percentage error ≈ 98.48%
Converting the absolute error to a positive percentage:
The absolute error is 98.48%, which is closest to 0.77%.
Therefore, the correct answer is option 'A' - 0.77%.
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