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Chapter 32, Problem 44PQ

(a)

To determine

The graph of ε versus t for each coil.

(a)

Expert Solution
Check Mark

Answer to Problem 44PQ

Plot for the induced emf in coil 1 is shown below.

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term, Chapter 32, Problem 44PQ , additional homework tip  1

Plot for the induced emf in coil 2 is shown below.

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term, Chapter 32, Problem 44PQ , additional homework tip  2

Plot for induced emf in coil 3 is shown below.

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term, Chapter 32, Problem 44PQ , additional homework tip  3

Explanation of Solution

As it is known that a three phase generator has 3 coils wound over a common armature, in away that each coil is set at an angle of 120° to the other two.

Therefore, a phase a difference of 120° occurs between 1, 2 and 2, 3 and a phase difference of 240° between 1, 3

Write the expression to calculate the induced emf in the coil.

    ε=ε0sin(ωt+ϕ)                               (I)

Here, ε is the induced emf, ε0 is the peak value of the induced emf, ω is the angular velocity and ϕ is  the initial phase of the coil when time is zero.

Write the expression to calculate the peak value of emf.

    ε=(2)εmax                                  (II)

Here, εmax is the rms value of the emf

Write the expression for the angular frequency.

    ω=2πf                        (III).

Here, f is the frequency.

Let the coil 1 be set such that when time is zero the emf induced is also zero.

Substitute 0 for ε and 0 for t in Equation (I).

    0=ε0sin(0+ϕ)sinϕ=0ϕ=0

Write the Equation for the emf of coil 1.

    ε=ε0sinωt                               (IV).

Convert degree in to radian

    120°=120°×π180°rad=2π3rad

Write the expression for induced emf in coil 2.

Substitute 2π3rad for ϕ in Equation (I).

    ε=ε0sin(ωt+2π3rad)                                 (V)

Convert degree in to radian

    240°=240°×π180°rad=4π3rad

Write the expression for induced emf in coil 3.

Substitute 4π3rad for ϕ in Equation (I).

    ε=ε0sin(ωt+4π3rad)                                 (VI)

Calculate the peak emf

Substitute 110V for εmax in Equation (II)

    ε=(2)110V=156V

Conclusion:

Calculate the angular frequency.

Substitute 60Hz for f in Equation (III).

    ω=2π×60Hz=377rad/sec

Calculate the equation of emf for coil 1.

Substitute 156V for ε0 and 377rad/sec for ω in Equation (IV).

    ε=156Vsin(377rad/sec×t)                             (VII)

Calculate the equation of emf for coil 2.

Substitute 156V for ε0 and 377rad/sec for ω in Equation (V).

    ε=156Vsin(377rad/sec×t+3rad)                 (VIII)

Calculate  the equation of emf for coil 3.

Substitute 156V for ε0 and 377rad/sec for ω in Equation (IV).

    ε=156Vsin(377rad/sec×t+3rad)                  (VI)

Draw the table to plot the graph at different time interval.

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term, Chapter 32, Problem 44PQ , additional homework tip  4

Plot for the induced emf in coil 1 is shown below.

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term, Chapter 32, Problem 44PQ , additional homework tip  5

Plot for the induced emf in coil 2 is shown below.

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term, Chapter 32, Problem 44PQ , additional homework tip  6

Plot for induced emf in coil 3 is shown below.

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term, Chapter 32, Problem 44PQ , additional homework tip  7

(b)

To determine

The ways in which a three phase generator is better than a one phase generator.

(b)

Expert Solution
Check Mark

Answer to Problem 44PQ

The three phase generator has higher efficiency and higher power factor compared to a one phase generator which is its major advantage over one phase generator.

Explanation of Solution

The advantage of three phase generator over a one phase generator are as follows.

  1. 1. The power output of a three phase generator is constant whereas the power generated by a one phase generator is pulsating that it is not constant and behaves in an alternating manner.
  2. 2. The three phase generator has higher power factor as compared to one phase generator.
  3. 3. The three phase generator has much higher efficiency as compared to the one phase motor.

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Chapter 32 Solutions

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term

Ch. 32 - Prob. 2PQCh. 32 - Prob. 3PQCh. 32 - Prob. 4PQCh. 32 - Prob. 5PQCh. 32 - Figure P32.6 shows three situations involving a...Ch. 32 - A rectangular loop of length L and width W is...Ch. 32 - The magnetic field through a square loop of wire...Ch. 32 - Prob. 9PQCh. 32 - Prob. 10PQCh. 32 - Suppose a uniform magnetic field is perpendicular...Ch. 32 - Prob. 12PQCh. 32 - A square conducting loop with side length a = 1.25...Ch. 32 - A The magnetic field in a region of space is given...Ch. 32 - A The magnetic field in a region of space is given...Ch. 32 - Prob. 16PQCh. 32 - Prob. 17PQCh. 32 - Prob. 18PQCh. 32 - A square loop with side length 5.00 cm is on a...Ch. 32 - A thin copper rod of length L rotates with...Ch. 32 - Figure P32.21 shows a circular conducting loop...Ch. 32 - Prob. 22PQCh. 32 - A square loop with side length L, mass M, and...Ch. 32 - Prob. 24PQCh. 32 - Prob. 25PQCh. 32 - Prob. 26PQCh. 32 - Prob. 27PQCh. 32 - A solenoid of area Asol produces a uniform...Ch. 32 - Two circular conductors are perpendicular to each...Ch. 32 - Two circular conducting loops labeled A and B are...Ch. 32 - Prob. 31PQCh. 32 - Prob. 32PQCh. 32 - Prob. 33PQCh. 32 - Prob. 34PQCh. 32 - Prob. 35PQCh. 32 - Find an expression for the current in the slide...Ch. 32 - The slide generator in Figure 32.14 (page 1020) is...Ch. 32 - Prob. 38PQCh. 32 - A thin conducting bar (60.0 cm long) aligned in...Ch. 32 - A stiff spring with a spring constant of 1200.0...Ch. 32 - A generator spinning at a rate of 1.20 103...Ch. 32 - Suppose you have a simple homemade AC generator...Ch. 32 - Prob. 43PQCh. 32 - Prob. 44PQCh. 32 - Prob. 45PQCh. 32 - Prob. 46PQCh. 32 - A square coil with a side length of 12.0 cm and 34...Ch. 32 - Prob. 48PQCh. 32 - Prob. 49PQCh. 32 - Prob. 50PQCh. 32 - Prob. 51PQCh. 32 - Prob. 52PQCh. 32 - Prob. 53PQCh. 32 - Prob. 54PQCh. 32 - Prob. 55PQCh. 32 - Prob. 56PQCh. 32 - Prob. 57PQCh. 32 - A step-down transformer has 65 turns in its...Ch. 32 - Prob. 59PQCh. 32 - Prob. 60PQCh. 32 - Prob. 61PQCh. 32 - Prob. 62PQCh. 32 - Prob. 63PQCh. 32 - A bar magnet is dropped through a loop of wire as...Ch. 32 - Prob. 65PQCh. 32 - Prob. 66PQCh. 32 - A circular coil with 75 turns and radius 12.0 cm...Ch. 32 - Each of the three situations in Figure P32.68...Ch. 32 - A square loop with sides 1.0 m in length is placed...Ch. 32 - Prob. 70PQCh. 32 - Two frictionless conducting rails separated by l =...Ch. 32 - Imagine a glorious day after youve finished...Ch. 32 - Prob. 73PQCh. 32 - A Figure P32.74 shows an N-turn rectangular coil...Ch. 32 - A rectangular conducting loop with dimensions w =...Ch. 32 - Prob. 76PQCh. 32 - A conducting rod is pulled with constant speed v...Ch. 32 - Prob. 78PQCh. 32 - A conducting single-turn circular loop with a...Ch. 32 - A metal rod of mass M and length L is pivoted...
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