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Chapter 32: 6. (page 924)

A 200 Ω resistor is connected to an AC source with E0=10 V. What is the peak current through the resistor if the emf frequency is (a) 100 Hz? (b) 100 kHz?

Short Answer

Expert verified

Result is: $I_{0} = 50 mA$

Step by step solution

01

Part (a) Step 1 : Given information

R = 200Ω

$ε_{0}$ =10V

Frequency=100Hz

02

Part (a) Step 2 : Simplify

Peak Current is given by $I = \frac{ε_{o}}{R^{}}$ , does not depend on frequency.

$I_{o} = \frac{ε_{o}}{R}$

$I_{o} = \frac{10 V}{200 Ω}$

$I_{0 = 0.05 A}$

$I_{0 = 50 m A}$

03

Part (b) Step 1 : Given information

R = 200Ω

$ε_{0}$ =10V

Frequency=100 kHz

04

Part (b) Step 2 : Simplify

Peak Current is given by $I_{o} = \frac{ε_{o}}{R}$ , does not depend on frequency.

$I_{o} = \frac{ε_{o}}{R}$

$I_{o} = \frac{10 V}{200 Ω}$

$I_{o} = 0.05 A$

$I_{0 = 50 m A}$

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Most popular questions from this chapter

The telecommunication circuit shown in FIGURE CP $32.71$ 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

$I = \frac{ε_{0}}{\sqrt{R^{2} + {(\frac{1}{X_{L}} - \frac{1}{X_{C}})}^{- 2}}}$

b. What is I in the limits $ω \to 0$ and $ω \to \infty$ ?

c. What is the resonance frequency $ω_{0}$ ? What is I at this frequency?

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

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf, three separate wires carry currents for the emfs $E_{1} = E_{0} \cos v t, E_{2} = E_{0_{}} \cos 1 v t + 120 °, a n d E_{3} = E_{0} \cos 1 v t - 120 °$ 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?

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?

What are $V_{R}$ and $V_{C}$ if the emf frequency in FIGURE is $10 kHz$ ?

See all solutions

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