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Chapter 32: Q. 2 (page 923)

The emf phasor in FIGURE EX32.2 is shown at t=15ms.

a. What is the angular frequency ω? Assume this is the first rotation.

b. What is the instantaneous value of the emf?

Short Answer

Expert verified

The angular frequency ωis 244rad/sand instantaneous value of the emf is-10V.

Step by step solution

01

Part (a) Step 1: Given information

We are given that time t=15ms, Eo=12Vand ∅=150∘(as the phasor rotates anticlockwise towards X-axis)

02

Part (a) Step 2: Calculation

As we know that-

E=E0cos(ωt+∅)

ωt=180∘+∅ωt=180∘+30∘ωt=210∘ (as phasor rotates anticlockwise)

Now converting degrees into radian

210∘=210∘πrad180∘=7πrad6

Now,

ωt=7πrad6ω(15×10-3)=7πrad6ω=244rad/s

03

Part (b) Step 1: Given information

We are given that-

E0=12V∅=150∘

04

Part (b) Step 2: Calculation

As we know that peak valueE0=12V will occur when ωt=0

So now in the expression,

E=E0cos(ωt+∅)E=12Vcos(0+150∘)E=-10V

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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, three separate wires carry currents for the emfs E1=E0cosvt,E2=E0cos1vt+120°,andE3=E0cos1vt-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 450MWof electric power, a realistic value.

a. What would be the current in each wire if the transmission voltage were E0=120Vrms?

b. In fact, transformers are used to step the transmission-line voltage up to 500kVrms. What is the current in each wire?

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

A low-pass filter consists of a 100mFcapacitor in series with a 159Ωresistor. The circuit is driven by an ACsource with a peak voltage of 5.00V.

a. What is the crossover frequency fc?

b. What is VCwhen f=12fc,fc and 2fc?

A series RLC circuit attached to a 120V/60Hzpower line draws a 2.4Arms current with a power factor of 0.87. What is the value of the resistor?

A series RLC circuit consists of a 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a 2.1mH inductor, and a 550nF capacitor. It is connected to a 50V rms oscillating voltage source with an adjustable frequency. An oscillating magnetic field is observed at a point 2.5mm from the center of one of the circuit wires, which is long and straight. What is the maximum magnetic field amplitude that can be generated?

FIGURE Q32.1shows emf phasors a, b, and c.

a. For each, what is the instantaneous value of the emf?

b. At this instant, is the magnitude of each emf increasing, decreasing, or holding constant?
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