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Difficulty: MediumElectromagnetic Induction

When a soft-iron core is inserted into an air-core solenoid connected to a constant-voltage alternating current (AC) source, the root-mean-square (rms) current flowing through the circuit increases.

Answer: Answer

Answer

The statement is False. Inserting a soft-iron core increases the self-inductance and inductive reactance of the coil, which decreases the rms current.
Inserting a soft-iron core raises the magnetic permeability, thereby increasing the coil's self-inductance (LL) and inductive reactance (XL=2πfLX_L = 2\pi f L). This higher reactance opposes current flow more strongly, causing the rms current to drop.

Step-by-Step Solution

1
Determine the effect of a soft-iron core on self-inductance.
Soft iron has high magnetic permeability, which concentrates magnetic flux lines and markedly increases the coil's self-inductance (LL).
Self-inductance is directly proportional to the magnetic permeability of the core material.
2
Relate self-inductance to inductive reactance in an AC circuit.
Inductive reactance is given by XL=2πfLX_L = 2\pi f L. An increase in LL produces a proportional increase in XLX_L.
Inductive reactance represents the opposition offered by an inductor to alternating current.
3
Calculate the impact on root-mean-square (rms) current.
Using Ohm's law for AC reactive circuits, Irms=VrmsXLI_{\text{rms}} = \frac{V_{\text{rms}}}{X_L}. Since XLX_L increases, IrmsI_{\text{rms}} decreases.
Current is inversely proportional to reactance for a constant supply voltage.

Key Concept

Self-Inductance and Inductive Reactance in AC Circuits
Estimated Time:1m 0s
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Topics

Electromagnetic Induction

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