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The voltage phaser of a circuit is 10∠15°V and the current phasor is 2∠−45° A. The active and reactive powers in the circuit are
- a)10W and 17.32VAR
- b)5W and 8.66VAR
- c)20W and 60VAR
- d)20√2W and 10√2VAR
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The voltage phaser of a circuit is 10∠15°V and the current phasor is ...
Hence, the correct option is (a).
Most Upvoted Answer
The voltage phaser of a circuit is 10∠15°V and the current phasor is ...
Given Data:
Voltage phasor (V) = 10∠15°V
Current phasor (I) = 2∠−45° A
Calculating Active Power (P):
Active power (P) = |V| * |I| * cos(θv - θi)
P = 10 * 2 * cos(15° - (-45°))
P = 10 * 2 * cos(60°)
P = 10 * 2 * 0.5
P = 10 W
Calculating Reactive Power (Q):
Reactive power (Q) = |V| * |I| * sin(θv - θi)
Q = 10 * 2 * sin(15° - (-45°))
Q = 10 * 2 * sin(60°)
Q = 10 * 2 * √3/2
Q ≈ 17.32 VAR
Therefore, the active power in the circuit is 10W and the reactive power is approximately 17.32VAR. Hence, option 'A' is the correct answer.
Voltage phasor (V) = 10∠15°V
Current phasor (I) = 2∠−45° A
Calculating Active Power (P):
Active power (P) = |V| * |I| * cos(θv - θi)
P = 10 * 2 * cos(15° - (-45°))
P = 10 * 2 * cos(60°)
P = 10 * 2 * 0.5
P = 10 W
Calculating Reactive Power (Q):
Reactive power (Q) = |V| * |I| * sin(θv - θi)
Q = 10 * 2 * sin(15° - (-45°))
Q = 10 * 2 * sin(60°)
Q = 10 * 2 * √3/2
Q ≈ 17.32 VAR
Therefore, the active power in the circuit is 10W and the reactive power is approximately 17.32VAR. Hence, option 'A' is the correct answer.
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