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Difficulty: MediumInductors and Transformers

An air-core inductor is connected in series with an alternating current (AC) voltage source. If a solid soft-iron core with high magnetic permeability is fully inserted into the center of the coil, how does this modification affect the coil's inductance and the overall circuit current?

  1. A
    Inductance increases, causing the circuit current to increase.
  2. B
    Inductance decreases, causing the circuit current to increase.
  3. Inductance increases, causing the circuit current to decrease.Answer
  4. D
    Inductance remains unchanged, but the circuit current drops to zero because iron blocks alternating current.

Answer

Inductance increases, causing the circuit current to decrease.
Inserting a soft-iron core with high magnetic permeability concentrates the magnetic lines of force inside the inductor. Because inductance is directly proportional to permeability (L=μN2AlL = \frac{\mu N^2 A}{l}), the inductance increases. In an AC circuit, inductive reactance is given by XL=2πfLX_L = 2\pi f L. As inductance increases, inductive reactance increases, providing greater opposition to alternating current. By Ohm's law (I=VXLI = \frac{V}{X_L}), the higher opposition causes the circuit current to decrease.

Step-by-Step Solution

1
Determine the effect of inserting an iron core on coil inductance.
The inductance (LL) increases significantly because the magnetic permeability (μ\mu) of soft iron is hundreds of times greater than that of air (L=μN2AlL = \frac{\mu N^2 A}{l}).
Inductance is directly proportional to the magnetic permeability of the core material.
2
Determine the relationship between inductance and inductive reactance in an AC circuit.
Inductive reactance (XLX_L) increases proportionally with inductance (XL=2πfLX_L = 2\pi f L).
Inductive reactance represents the total counter-electromotive force opposition to alternating current.
3
Apply Ohm's law for AC circuits to determine current change.
Circuit current (II) decreases (I=VXLI = \frac{V}{X_L}).
Under constant source voltage, an increase in circuit reactance reduces total current flow.

Key Concept

Magnetic core permeability increases inductance and inductive reactance, which reduces AC circuit current.
Estimated Time:1m 0s
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Topics

Inductors and Transformers

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