Answers to Even-numbered Conceptual Questions
Light will attain its maximum brightness 120 times per second; that is, twice per cycle.
The reason for the factor of two per cycle is that the current reverses direction every cycle,
and the bulb will be brightest when the current is a maximum in either direction.
The intensity of the light bulb will decrease if the frequency of the generator is increased.
The reason is that inductors oppose any change in current, and the more rapidly the
current changes the stronger the opposition.
Thus, as the frequency is increased, the
current in the circuit decreases, and the light bulb becomes dimmer.
Current and voltage are not always in phase in an ac circuit because capacitors and
inductors respond not to the current itself – as a resistor does – but to the charge
(capacitor) or to the rate of change of the current (inductor).
The charge takes time to
build up; therefore, a capacitor’s voltage lags behind the current. The rate of change of
current is greatest when the current is least; therefore, an inductor’s voltage leads the
Resistors, of course, are always in phase with the current.
As the frequency is increased, the inductive reactance increases as well.
frequencies greater than the resonance frequency of an
circuit, the inductive reactance
is greater than the capacitive reactance.
As a result, the inductor dominates, and the
voltage leads the current.
This means that the phase angle,
In a dc circuit the frequency is zero, which means that the inductive reactance is zero
Therefore, the inductor has no effect at all on the current in the circuit, nor on the
brightness of the bulb.
In a dc circuit, an ideal inductor is the same as a piece of zero-
At low frequency, the capacitor is essentially the same as a break in the circuit, whereas
the inductor is essentially an ideal wire.
It follows, then, that more current will be
supplied by the generator if the inductor and the capacitor are connected in parallel.
Recall that charge in an
circuit is the analog of position in a mass-spring system.
Therefore, the current – which is the rate of change of charge – is analogous to the
velocity – which is the rate of change of position.
(See Table 24-2.)
All that is required for their resonance frequencies to be the same is for the product
to be the same.
(See Equation 24-18.)
At high frequency, we can replace the inductor with an open circuit.
At low frequency,
we can replace the capacitor with an open circuit.
In either case, the effective resistance
of the circuit is
; therefore, the current is the same.
At high frequency, the capacitor behaves essentially the same as an ideal wire, which
means that the effective resistance of the circuit is
At low frequency, the capacitor is
basically a break in the circuit.
In this case, the effective resistance of the circuit is
follows that the current in the circuit is greater at high frequency.