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A lossy capacitor with a loss angle of 0.01 radian draws a current of 0.5 A when supplied at 1000V from a sinusoidal voltage source. The active power consumed by the capacitor is-
- a)5 W
- b)10 W
- c)2 W
- d)1 W
Correct answer is option 'A'. Can you explain this answer?
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A lossy capacitor with a loss angle of 0.01 radian draws a current of...
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Lossy Capacitor:
A lossy capacitor is a type of capacitor that has a non-zero loss angle (also known as the dissipation factor or power factor). This means that the capacitor has some amount of resistance, which results in energy losses and power consumption. The loss angle is defined as the phase difference between the voltage across the capacitor and the current flowing through it.
Given Parameters:
- Loss angle (δ) = 0.01 radian
- Current (I) = 0.5 A
- Voltage (V) = 1000 V
Calculating the Active Power Consumed:
The active power consumed by the capacitor can be calculated using the formula:
P = VI * cos(δ)
Where:
- P is the active power consumed (in watts)
- V is the voltage across the capacitor (in volts)
- I is the current flowing through the capacitor (in amperes)
- δ is the loss angle (in radians)
Substituting the given values into the formula:
P = 1000V * 0.5A * cos(0.01 radian)
P = 500 W * cos(0.01 radian)
P ≈ 500 W * 1 (since cos(0.01 radian) is approximately equal to 1)
P ≈ 500 W
Therefore, the active power consumed by the capacitor is approximately 500 watts.
Answer Verification:
The options given are:
a) 5 W
b) 10 W
c) 2 W
d) 1 W
Comparing the calculated value of 500 W with the given options, we can see that the correct answer is option 'a' (5 W).
Therefore, the active power consumed by the capacitor is 5 watts.
A lossy capacitor is a type of capacitor that has a non-zero loss angle (also known as the dissipation factor or power factor). This means that the capacitor has some amount of resistance, which results in energy losses and power consumption. The loss angle is defined as the phase difference between the voltage across the capacitor and the current flowing through it.
Given Parameters:
- Loss angle (δ) = 0.01 radian
- Current (I) = 0.5 A
- Voltage (V) = 1000 V
Calculating the Active Power Consumed:
The active power consumed by the capacitor can be calculated using the formula:
P = VI * cos(δ)
Where:
- P is the active power consumed (in watts)
- V is the voltage across the capacitor (in volts)
- I is the current flowing through the capacitor (in amperes)
- δ is the loss angle (in radians)
Substituting the given values into the formula:
P = 1000V * 0.5A * cos(0.01 radian)
P = 500 W * cos(0.01 radian)
P ≈ 500 W * 1 (since cos(0.01 radian) is approximately equal to 1)
P ≈ 500 W
Therefore, the active power consumed by the capacitor is approximately 500 watts.
Answer Verification:
The options given are:
a) 5 W
b) 10 W
c) 2 W
d) 1 W
Comparing the calculated value of 500 W with the given options, we can see that the correct answer is option 'a' (5 W).
Therefore, the active power consumed by the capacitor is 5 watts.
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