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Chapter 32: Q. 62 (page 926)

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?

Short Answer

Expert verified

The rate at which energy is dissipated in each bulb is

$I = 0.2 A, P_{1} = 14.4 W, P_{2} = 9.6 W$

Step by step solution

01

Given Information

We have been given that light bulbs of $40 W, 60 W a n d 100 W$ are connected to a $120 V / 60 H z$ powerline and we have to find the rate at which energy is dissipated in each bulb.

02

Simplification

For the bulb of $40 W$ :

$P_{1} = \frac{V^{2}}{R_{1}}$

For the $60 W$ bulb:

$P_{2} = \frac{V^{2}}{R_{2}}$

$R_{2} = 240 惟$

The total resistance is:

$600 o h m$

The power dissipation in $40 W$ bulb is:

$P_{d i s_{1}} = 14.4 W$

The power dissipation in bulb is:

$P_{d i s_{2}} = 9.6 W$

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Most popular questions from this chapter

Consider the parallel RLC circuit shown in $F I G U R E C P 32.72$ .

a. Show that the current drawn from the emf is

$I = 蔚_{o} \sqrt{\frac{1}{R^{2}} + {(\frac{1}{蝇 L} - 蝇 C)}^{2}}$

Hint: Start with a phasor that is common to all three circuit elements.

b. What is $I$ in the limits $蝇鈫� 0$ and $蝇鈫� 鈭�$ ?

c. Find the frequency for which $I$ is a minimum.

d. Sketch a graph of $I$ versus $蝇$ .

A high-pass $R C$ filter with a crossover frequency of $1000 H z$ uses a $100 鈩�$ resistor. What is the value of the capacitor?

For the circuit of FIGURE EX32.32,

a. What is the resonance frequency, in both rad/s and Hz?

b .Find $V_{R}$ and $V_{L}$ at resonance.

c. How can $V_{L}$ be larger than $蔚_{o}$ ? Explain.

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf, three separate wires carry currents for the emfs $E_{1} = E_{0} \cos v t, E_{2} = E_{0_{}} \cos 1 v t + 120 掳, a n d E_{3} = E_{0} \cos 1 v t - 120 掳$ over three parallel wires, each of which supplies one-third of the power. This is why the long-distance transmission lines you see in the countryside have three wires. Suppose the transmission lines into a city supply a total of $450 M W$ of electric power, a realistic value.

a. What would be the current in each wire if the transmission voltage were $E_{0} = 120 V_{r m s}$ ?

b. In fact, transformers are used to step the transmission-line voltage up to $500 k V_{r m s}$ . What is the current in each wire?

c. Big transformers are expensive. Why does the electric company use step-up transformers?

A low-pass $R C$ filter has a crossover frequency $f_{c} = 200$ Hz.What is $f_{c}$ if:

a. The resistance $R$ is doubled?

b. The capacitance $C$ is doubled?

c. The peak emf $E_{0}$ is doubled?

See all solutions

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