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Chapter 32: Q. 71 (page 927)

The telecommunication circuit shown in $F I G U R E C P 32.71$ has a parallel inductor and capacitor in series with a resistor.
a. Use a phasor diagram to show that the peak current through the resistor is
$I = \frac{蔚_{0}}{\sqrt{R^{2} + {(\frac{1}{X_{L}} - \frac{1}{X_{C}})}^{- 2}}}$
Hint: Start with the inductor phasor $谓_{L}$ .
b. What is $I$ in the limits $蝇鈫� 0$ and $蝇鈫� 鈭�$ ?
c. What is the resonance frequency $蝇_{o}$ ? What is $I$ at this frequency?

Short Answer

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(a)

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01

Part(a) Step 1: Given information

We have been given that

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Most popular questions from this chapter

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf $E = E_{0} \cos v t$ , three separate wires carry currents for the emfs $E_{1} = E_{0} \cos v t, E_{2} = E_{0} \cos 1 v t + 120 掳, a n d E_{3} = E_{0} \cos 1 v t - 120 掳$ . This is why the long-distance transmission lines you see in the countryside have three parallel wires, as do many distribution lines within a city.

a. Draw a phasor diagram showing phasors for all three phases of a three-phase emf.

b. Show that the sum of the three phases is zero, producing what is referred to as neutral. In single-phase electricity, provided by the familiar electric outlets in your home, one side of the outlet is neutral, as established at a nearby electrical substation. The other, called the hot side, is one of the three phases. (The round opening is connected to ground.)

c. Show that the potential difference between any two of the phases has the rms value where is the familiar single-phase rms voltage. Evaluate this potential difference for . Some high-power home appliances, especially electric clothes dryers and hot-water heaters, are designed to operate between two of the phases rather than between one phase and neutral. Heavy-duty industrial motors are designed to operate from all three phases, but full three-phase power is rare in residential or office use.

Lightbulbs labeled $40 W, 60 W$ and $100 W$ are connected to a $120 V / 60 H z$ power line as shown in the figure .What is the rate at which energy is dissipated in each bulb?

A capacitor is connected across an oscillating emf. The peak current through the capacitor is $2 A 鈥� .$ What is the peak current if:

a. The capacitance $C$ is doubled?

b. The peak emf $E 0$ is doubled?

c. The frequency $v$ is doubled?

A high-pass filter consists of a $1.59 m F$ capacitor in series with a $100 鈩�$ resistor. The circuit is driven by an $A C$ source with a peak voltage of $5.00 V$ .

a. What is the crossover frequency $f_{c}$ ?

b. What is $V_{R}$ when $f = \frac{1}{2} f_{c}, f_{c}$ , and $2 f_{c}$ ?

A series $R C$ circuit is built with a $12 k 鈩�$ resistor and a parallel-plate capacitor with $15 - c m -$ diameter electrodes. Alocalid="1649923196754" $12 V, 36 k H z$ source drives a peak current of $0.65 m A$ through the circuit. What is the spacing between the capacitor plates?

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