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A coil having 90 turns is connected to a 120 V, 60 Hz source. If the effective value of the magnetizing current is 4 A, then calculate the value of inductance of the coil.
  • a)
    79.6 mH
  • b)
    121.2 mH
  • c)
    32.2 mH
  • d)
    83.16 mH
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A coil having 90 turns is connected to a 120 V, 60 Hz source. If the e...
Given that, emf (E) = 120 V
Magnetizing current (I) = 4 A
Frequency (f) = 60 Hz
Reactance = 120/4 = 30 Ω
We know that, XL = 2πfL
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Most Upvoted Answer
A coil having 90 turns is connected to a 120 V, 60 Hz source. If the e...
To calculate the value of inductance of the coil, we can use the formula:

Inductance (L) = (V / (2 * π * f * I))

where:
V = Voltage (120 V)
f = Frequency (60 Hz)
I = Current (4 A)

Now, let's calculate the value of inductance step by step:

Step 1: Calculate the angular frequency (ω)
The angular frequency is given by the formula:

ω = 2 * π * f

Substituting the given values, we get:

ω = 2 * 3.14 * 60
ω = 376.8 rad/s

Step 2: Calculate the inductance (L)
Using the formula for inductance, we have:

L = (V / (2 * π * f * I))

Substituting the given values, we get:

L = (120 / (2 * 3.14 * 60 * 4))
L = 120 / 1507.2
L = 0.0796 H

Step 3: Convert the inductance to millihenries (mH)
The value of inductance is given in henries, but the options are given in millihenries. To convert the value to millihenries, we multiply by 1000:

L = 0.0796 * 1000
L = 79.6 mH

Therefore, the value of inductance of the coil is 79.6 mH, which corresponds to option A.
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Question Description
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