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The inductive reactance ($X_L$) of a pure inductor is directly proportional to:

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Explanation

The example calculates inductive reactance as $X_L = 2\pi \nu L$. This formula clearly shows that inductive reactance is directly proportional to the frequency ($\nu$) of the AC source.

In a purely inductive AC circuit, which of the following statements about the phase relationship between voltage and current is correct?

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Explanation

The text mentions, 'in the case of an inductor, the current lags the voltage by $\pi/2$'. This is equivalent to saying voltage leads current by $\pi/2$.

A pure inductor of 25.0 mH is connected to a 220 V AC source with a frequency of 50 Hz. What is the inductive reactance?

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Explanation

From Example 7.2: $X_L = 2\pi \nu L = 2 \times 3.14 \times 50 \times 25 \times 10^{-3} \Omega = 7.85 \Omega$.

Phasors are used in AC circuits primarily to:

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Explanation

The text states, 'In order to show phase relationship between voltage and current in an ac circuit, we use the notion of phasors. The analysis of an ac circuit is facilitated by the use of a phasor diagram.'

In a purely inductive AC circuit, according to Kirchhoff's loop rule, if the voltage across the source is $v = v_m \sin \omega t$, then the equation for the self-induced EMF is:

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Explanation

From the section 'AC VOLTAGE APPLIED TO AN INDUCTOR', it is stated that 'the self-induced Faraday emf in the inductor' is $L \frac{di}{dt}$. Applying Kirchhoff's loop rule for a pure inductor, $v - L \frac{di}{dt} = 0$, hence $v = L \frac{di}{dt}$.

What happens to the inductive reactance of an inductor if an iron rod is inserted into its interior, assuming negligible resistance?

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Explanation

Example 7.5 states, 'As the iron rod is inserted, the magnetic field inside the coil magnetizes the iron increasing the magnetic field inside it. Hence, the inductance of the coil increases. Consequently, the inductive reactance of the coil increases.'

When an iron rod is inserted into the inductor of a circuit containing a light bulb in series with an AC source (and the inductor), what happens to the glow of the light bulb?

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Explanation

As per Example 7.5: 'As a result, a larger fraction of the applied ac voltage appears across the inductor, leaving less voltage across the bulb. Therefore, the glow of the light bulb decreases.'

A purely inductive circuit is an ideal circuit condition. In reality, inductors usually have:

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Explanation

The text mentions, 'Usually, inductors have appreciable resistance in their windings, but we shall assume that this inductor has negligible resistance' (for the purpose of an ideal purely inductive circuit analysis).

Which of the following conditions is necessary for the production of electromagnetic waves?

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Explanation

According to Maxwell's theory, accelerated charges radiate electromagnetic waves. Neither stationary charges nor charges in uniform motion can be sources of electromagnetic waves. (Context: 'It is an important result of Maxwell’s theory that accelerated charges radiate electromagnetic waves.')

The relationship between the magnitude of the electric field ($E_0$) and the magnetic field ($B_0$) in an electromagnetic wave in vacuum is given by:

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Explanation

From Maxwell's equations, it is seen that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as $B_0 = (E_0/c)$, which rearranges to $E_0 = B_0c$. (Context: 'It is also seen from Maxwell’s equations that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as $B_0 = (E_0/c)$ (8.10)')

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