Explanation Given data: Refer to the given figure in the textbook for the three-phase circuit. Calculation: Consider the expression for the per phase impedance Z ϕ . Z ϕ = | Z | ∠ θ (1) Write the expression for the per phase impedance Z ϕ for a-phase. Z ϕ = V AN I aA (2) Compare Equations (1) and (2). | Z | ∠ θ = V AN I aA (3) From Equation (3), consider that the impedance angle ( θ ) is the angle between the phase voltage V AN and current I aA . θ = ∠ V AN − ∠ I aA Consider that the angle ( θ 1 ) is the phase angle between the line voltage V AB and the line current I aA . θ 1 = ∠ V AB − ∠ I aA (4) Consider the expression for the angle of line voltage V AB in the positive phase sequence. ∠ V AB = ∠ V AN + 30 ° (5) Substitute Equation (5) in (4). θ 1 = ( ∠ V AN + 30 ° ) − ∠ I aA = ( ∠ V AN − ∠ I aA ) + 30 ° Substitute θ for ∠ V AN − ∠ I aA . θ 1 = θ + 30 ° (6) Write the expression for the per phase impedance Z ϕ for c-phase. Z ϕ = V CN I cC (7) Compare Equations (1) and (7). | Z | ∠ θ = V CN I cC (8) From Equation (8), consider that the impedance angle ( θ ) is the angle between the voltage V CN and current I cC

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Synchronous Motor

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Chapter 11, Problem 46P

To determine

Derive the expression for the phase angles θ1 and θ2.

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Chapter 11, Problem 45P

Chapter 11, Problem 47P

Chapter 11 Solutions

EBK ELECTRIC CIRCUITS

Ch. 11.3 - The voltage from A to N in a balanced three-phase...Ch. 11.3 - Prob. 2AP Ch. 11.4 - Prob. 4AP Ch. 11.4 - Prob. 5AP Ch. 11.4 - Prob. 6AP Ch. 11.4 - Prob. 7AP Ch. 11.5 - Prob. 8AP Ch. 11.5 - Prob. 9AP Ch. 11 - Prob. 1P Ch. 11 - Prob. 3P

Ch. 11 - Prob. 4P Ch. 11 - Repeat Problem 11.4 but assume that the...Ch. 11 - Prob. 6P Ch. 11 - Find I0 in the circuit in Fig. P11.7. Find...Ch. 11 - Find the rms value of Io in the unbalanced...Ch. 11 - The time-domain expressions for three...Ch. 11 - Prob. 10P Ch. 11 - The magnitude of the line voltage at the terminals...Ch. 11 - A balanced Δ-connected load has an impedance of...Ch. 11 - A balanced, three-phase circuit is characterized...Ch. 11 - Prob. 15P Ch. 11 - In a balanced three-phase system, the source is a...Ch. 11 - Prob. 17P Ch. 11 - The impedance Z in the balanced three-phase...Ch. 11 - For the circuit shown in Fig. P11.20, find the...Ch. 11 - A balanced three-phase Δ-connected source is shown...Ch. 11 - Prob. 22P Ch. 11 - Fine the rms magnitude and the phase angle of ICA...Ch. 11 - Prob. 24P Ch. 11 - Prob. 25P Ch. 11 - The line-to-neutral voltage at the terminals of...Ch. 11 - Prob. 27P Ch. 11 - Prob. 28P Ch. 11 - Prob. 29P Ch. 11 - Calculate the complex power in each phase of the...Ch. 11 - Prob. 31P Ch. 11 - Prob. 32P Ch. 11 - Prob. 33P Ch. 11 - Prob. 34P Ch. 11 - Prob. 35P Ch. 11 - Three balanced three-phase loads are connected in...Ch. 11 - Prob. 37P Ch. 11 - Prob. 38P Ch. 11 - Prob. 40P Ch. 11 - Prob. 41P Ch. 11 - Prob. 42P Ch. 11 - Prob. 43P Ch. 11 - Prob. 44P Ch. 11 - Prob. 45P Ch. 11 - Prob. 46P Ch. 11 - Prob. 47P Ch. 11 - Prob. 48P Ch. 11 - Prob. 49P Ch. 11 - Prob. 50P Ch. 11 - Prob. 51P Ch. 11 - Find the reading of each wattmeter in the circuit...Ch. 11 - Prob. 53P Ch. 11 - Prob. 54P Ch. 11 - Prob. 55P Ch. 11 - Prob. 56P Ch. 11 - Prob. 57P Ch. 11 - Prob. 58P Ch. 11 - Prob. 59P Ch. 11 - Assume in Problem 11.59 that when the load drops...

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