To determine Prove that the given expressions of Δ conductances G a , G b , and G c as functions of three Y conductances G 1 , G 2 , and G 3 . Explanation Given data: Consider the general expressions of Δ conductances. G a = 1 R a (1) G b = 1 R b (2) G c = 1 R c (3) Consider the general expressions of Y conductances. G 1 = 1 R 1 (4) G 2 = 1 R 2 (5) G 3 = 1 R 3 (6) Calculation: Consider the star-delta resistance conversion formula for resistance R a . R a = R 1 R 2 + R 2 R 3 + R 1 R 3 R 1 (7) Substitute Equation (7) in (1). G a = 1 R 1 R 2 + R 2 R 3 + R 1 R 3 R 1 G a = R 1 R 1 R 2 + R 2 R 3 + R 1 R 3 (8) Re-arrange Equation (4). R 1 = 1 G 1 (9) Re-arrange Equation (5). R 2 = 1 G 2 (10) Re-arrange Equation (6). R 3 = 1 G 3 (11) Substitute Equations (9), (10), and (11) in (8). G a = 1 G 1 ( 1 G 1 ) ( 1 G 2 ) + ( 1 G 2 ) ( 1 G 3 ) + ( 1 G 1 ) ( 1 G 3 ) = 1 G 1 G 3 + G 1 + G 2 G 1 G 2 G 3 = 1 G 1 ( G 1 G 2 G 3 ) G 1 + G 2 + G 3 G a = G 2 G 3 G 1 + G 2 + G 3 (12) Consider the star-delta resistance conversion formula for resistance R b . R b = R 1 R 2 + R 2 R 3 + R 1 R 3 R 2 (13) Substitute Equation (13) in (2). G b = 1 R 1 R 2 + R 2 R 3 + R 1 R 3 R 2 G b = R 2 R 1 R 2 + R 2 R 3 + R 1 R 3 (14) Substitute Equations (9), (10), and (11) in (14)

Electrical Circuits and Modified MasteringEngineering - With Access

10th Edition

ISBN: 9780133992793

Author: NILSSON

Publisher: PEARSON

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Chapter 3, Problem 64P

To determine

Prove that the given expressions of Δ conductances Ga, Gb, and Gc as functions of three Y conductances G1, G2, and G3.

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Electrical Circuits and Modified MasteringEngineering - With Access

Ch. 3.2 - For the circuit shown, find (a) the voltage υ, (b)...Ch. 3.3 - Find the no-load value of υo in the circuit...Ch. 3.3 - Find the value of R that will cause 4 A of...Ch. 3.4 - Use voltage division to determine the voltage υo...Ch. 3.5 - a. Find the current in the circuit shown. b. If...Ch. 3.5 - Find the voltage υ across the 75 kΩ resistor in...Ch. 3.6 - The bridge circuit shown is balanced when R1 = 100...Ch. 3.7 - Use a Y-to-Δ transformation to find the voltage υ...Ch. 3 - Prob. 1P Ch. 3 - Find the power dissipated in each resistor in the...

Ch. 3 - For each of the circuits shown in Fig....Ch. 3 - For each of the circuits shown in Fig....Ch. 3 - Prob. 5P Ch. 3 - Prob. 6P Ch. 3 - Prob. 7P Ch. 3 - Find the equivalent resistance Rab each of the...Ch. 3 - Prob. 9P Ch. 3 - Prob. 11P Ch. 3 - Prob. 12P Ch. 3 - In the voltage-divider circuit shown in Fig. P...Ch. 3 - The no-load voltage in the voltage-divider circuit...Ch. 3 - Assume the voltage divider in Fig. P3.14 has been...Ch. 3 - Find the power dissipated in the resistor in the 5...Ch. 3 - For the current-divider circuit in Fig. P3.19...Ch. 3 - Specify the resistors in the current-divider...Ch. 3 - There is often a need to produce more than one...Ch. 3 - Show that the current in the kth branch of the...Ch. 3 - Prob. 23P Ch. 3 - Look at the circuit in Fig. P3.1 (d). Use current...Ch. 3 - Prob. 25P Ch. 3 - Prob. 26P Ch. 3 - Attach a 6 V voltage source between the terminals...Ch. 3 - Find the voltage x in the circuit in Fig. P3.28...Ch. 3 - Find υo in the circuit in Fig. P3.31 using voltage...Ch. 3 - Find υ1 and υ2 in the circuit in Fig. P3.30 using...Ch. 3 - Prob. 31P Ch. 3 - For the circuit in Fig. P3.29, calculate i1 and i2...Ch. 3 - A d'Arsonval ammeter is shown in Fig....Ch. 3 - A shunt resistor and a 50 mV. 1 mA d’Arsonval...Ch. 3 - A d’Arsonval movement is rated at 2 mA and 200 mV....Ch. 3 - Prob. 36P Ch. 3 - A d’Arsonval voltmeter is shown in Fig. P3.37....Ch. 3 - Suppose the d’Arsonval voltmeter described in...Ch. 3 - The ammeter in the circuit in Fig. P3. 39 has a...Ch. 3 - The ammeter described in Problem 3.39 is used to...Ch. 3 - The elements in the circuit in Fig2.24. have the...Ch. 3 - Prob. 42P Ch. 3 - Prob. 43P Ch. 3 - The voltmeter shown in Fig. P3.42 (a) has a...Ch. 3 - The voltage-divider circuit shown in Fig. P3.44 is...Ch. 3 - Assume in designing the multirange voltmeter shown...Ch. 3 - Prob. 47P Ch. 3 - Design a d'Arsonval voltmeter that will have the...Ch. 3 - Prob. 49P Ch. 3 - Prob. 50P Ch. 3 - Prob. 51P Ch. 3 - Prob. 52P Ch. 3 - Find the detector current id in the unbalanced...Ch. 3 - Find the current and power supplied by the 40 V...Ch. 3 - Find the current and power supplied by the 40 V...Ch. 3 - Find the current and power supplied by the 40 V...Ch. 3 - Find the equivalent resistance Rab in the circuit...Ch. 3 - Use a Δ-to-Y transformation to find the voltages...Ch. 3 - Find the resistance seen by the ideal voltage...Ch. 3 - Prob. 61P Ch. 3 - Find io and the power dissipated in the 140Ω...Ch. 3 - Prob. 63P Ch. 3 - Show that the expressions for Δ conductances as...Ch. 3 - Prob. 65P Ch. 3 - Prob. 66P Ch. 3 - Prob. 67P Ch. 3 - The design equations for the bridged-tee...Ch. 3 - Prob. 69P Ch. 3 - Prob. 70P Ch. 3 - Prob. 71P Ch. 3 - Prob. 72P Ch. 3 - Prob. 73P Ch. 3 - Prob. 74P Ch. 3 - Prob. 75P

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