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Difficulty: MediumInductors and Transformers

An inductor with an inductance of 2 H2\text{ H} is connected across an alternating current (AC\text{AC}) signal generator. If the generator frequency is doubled while maintaining a constant output voltage, how will the inductive reactance of the coil and the circuit current change?

  1. A
    The inductive reactance is halved, and the circuit current doubles.
  2. The inductive reactance doubles, and the circuit current is halved.Answer
  3. C
    The inductive reactance doubles, and the circuit current doubles.
  4. D
    The inductive reactance remains constant, and the circuit current drops to zero.

Answer

The inductive reactance doubles, and the circuit current is halved.
Inductive reactance is defined by the relationship XL=2πfLX_L = 2\pi f L. When the AC frequency (ff) is doubled, the inductive reactance doubles because of their direct linear relationship. According to Ohm's law for AC circuits (I=VXLI = \frac{V}{X_L}), increasing the total opposition by a factor of 22 at a constant voltage reduces the alternating current to half its original value.

Step-by-Step Solution

1
Determine the effect of frequency on inductive reactance
The inductive reactance (XLX_L) doubles.
Inductive reactance is calculated using the formula XL=2πfLX_L = 2\pi f L. Since XLX_L is directly proportional to frequency (ff), multiplying the frequency by 22 doubles the inductive reactance.
2
Determine the effect of changed reactance on circuit current using Ohm's law for AC circuits
The current (II) is reduced to one-half of its initial value.
Current in an inductive AC circuit is governed by I=VXLI = \frac{V}{X_L}. With voltage (VV) held constant, current is inversely proportional to inductive reactance (XLX_L). Doubling the reactance cuts the current in half.

Key Concept

Inductive Reactance and Frequency Relationship in AC Circuits
Estimated Time:1m 0s
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Topics

Inductors and Transformers

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