EBK ELECTRIC CIRCUITS
EBK ELECTRIC CIRCUITS
10th Edition
ISBN: 8220100801792
Author: Riedel
Publisher: YUZU
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Chapter 11, Problem 1P

a)

To determine

Find the phase sequence for the given set of voltages.

a)

Expert Solution
Check Mark

Answer to Problem 1P

The phase sequence is abc sequence.

Explanation of Solution

Given data:

Consider the set of voltages.

va=137cos(ωt+63°)V        (1)

vb=137cos(ωt57°)V        (2)

vc=137cos(ωt+183°)V        (3)

Calculation:

Convert the voltage in Equation (1) from cosine voltage form to phasor form.

Va=13763°V{Vmcos(ωt+θ)=Vmθ}

Convert the voltage in Equation (2) from cosine voltage form to phasor form.

Vb=13757°V

Convert the voltage in Equation (3) from cosine voltage form to phasor form.

Vc=137183°V

Subtract the phase angle of a-phase from all the phase angles of Va, Vb, and Vc.

Va=63°63°

Va=0°        (4)

Vb=57°63°

Vb=120°        (5)

And

Vc=183°63°

Vc=120°        (6)

From Equations (4), (5), and (6), the voltage at phase-b lags a-phase voltage by 120° and c-phase voltage leads a-phase voltage by 120°. Therefore, this phase relationship is abc phase sequence or positive phase sequence.

Conclusion:

Thus, the phase sequence is abc sequence.

b)

To determine

Find the phase sequence for the given set of voltages.

b)

Expert Solution
Check Mark

Answer to Problem 1P

The phase sequence is acb sequence.

Explanation of Solution

Given data:

Consider the set of voltages.

va=820cos(ωt36°)V        (7)

vb=820cos(ωt+84°)V        (8)

vc=820sin(ωt66°)V

vc=820cos(ωt156°)V        (9)

Calculation:

Convert the voltage in Equation (7) from cosine voltage form to phasor form.

Va=82036°V{Vmcos(ωt+θ)=Vmθ}

Convert the voltage in Equation (8) from cosine voltage form to phasor form.

Vb=82084°V

Convert the voltage in Equation (9) from cosine voltage form to phasor form.

Vc=82066°V

Subtract the phase angle of a-phase from all the phase angles of Va, Vb, and Vc.

Va=36°(36°)

Va=0°        (10)

Vb=84°(36°)

Vb=120°        (11)

And

Vc=156°(36°)

Vc=120°        (12)

From Equations (10), (11), and (12), the voltage at phase-b leads a-phase voltage by 120° and c-phase voltage lags a-phase voltage by 120°. Therefore, this phase relationship is acb phase sequence or negative phase sequence.

Conclusion:

Thus, the phase sequence is acb sequence.

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Chapter 11 Solutions

EBK ELECTRIC CIRCUITS

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