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Two sinusoidal currents are given by i1 = 100 sin (wt + p / 3) and
i2 = 150 sin (wt + p / 4) The phase difference between them is ......degrees.
- a)15
- b)50
- c)60
- d)105
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two sinusoidal currents are given by i1 = 100 sin (wt + p / 3) andi2 =...
Solution:
Given that,
i1 = 100 sin (wt p / 3)
i2 = 150 sin (wt p / 4)
To find the phase difference between them, we can use the formula:
Δφ = φ2 - φ1
where Δφ is the phase difference and φ1 and φ2 are the phase angles of i1 and i2, respectively.
Let's first find the phase angle of i1:
i1 = 100 sin (wt p / 3)
Comparing with the general equation of a sinusoidal current:
i = Im sin (wt + φ)
we can see that Im = 100 and φ = p / 3.
Therefore, the phase angle of i1 is φ1 = p / 3.
Now, let's find the phase angle of i2:
i2 = 150 sin (wt p / 4)
Comparing with the general equation of a sinusoidal current:
i = Im sin (wt + φ)
we can see that Im = 150 and φ = p / 4.
Therefore, the phase angle of i2 is φ2 = p / 4.
Substituting these values in the formula for phase difference, we get:
Δφ = φ2 - φ1
= (p / 4) - (p / 3)
= (3p - 4p) / 12
= -p / 12
Converting to degrees, we get:
Δφ = (-p / 12) × (180 / p)
= -15°
Since the phase difference cannot be negative, we take its absolute value:
|Δφ| = 15°
Therefore, the phase difference between i1 and i2 is 15°.
Hence, option A is the correct answer.
Given that,
i1 = 100 sin (wt p / 3)
i2 = 150 sin (wt p / 4)
To find the phase difference between them, we can use the formula:
Δφ = φ2 - φ1
where Δφ is the phase difference and φ1 and φ2 are the phase angles of i1 and i2, respectively.
Let's first find the phase angle of i1:
i1 = 100 sin (wt p / 3)
Comparing with the general equation of a sinusoidal current:
i = Im sin (wt + φ)
we can see that Im = 100 and φ = p / 3.
Therefore, the phase angle of i1 is φ1 = p / 3.
Now, let's find the phase angle of i2:
i2 = 150 sin (wt p / 4)
Comparing with the general equation of a sinusoidal current:
i = Im sin (wt + φ)
we can see that Im = 150 and φ = p / 4.
Therefore, the phase angle of i2 is φ2 = p / 4.
Substituting these values in the formula for phase difference, we get:
Δφ = φ2 - φ1
= (p / 4) - (p / 3)
= (3p - 4p) / 12
= -p / 12
Converting to degrees, we get:
Δφ = (-p / 12) × (180 / p)
= -15°
Since the phase difference cannot be negative, we take its absolute value:
|Δφ| = 15°
Therefore, the phase difference between i1 and i2 is 15°.
Hence, option A is the correct answer.
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Two sinusoidal currents are given by i1 = 100 sin (wt + p / 3) andi2 =...
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