To determine Calculate the value of voltage v in the given circuit using Y-to-Δ transformation. Explanation Formula used: Write the formulae for the conversion of Y-to-Δ connection. R a = R 1 R 2 + R 2 R 3 + R 3 R 1 R 1 (1) R b = R 1 R 2 + R 2 R 3 + R 3 R 1 R 2 . (2) R c = R 1 R 2 + R 2 R 3 + R 3 R 1 R 3 . (3) Here, R 1 , R 2 , and R 3 are the resistors connected in star connection. R a , R b , and R c are the resistors connected in delta connection. Calculation: The given circuit with the representation of delta-connected resistors is shown in Figure 1. Substitute 20 Ω for R 1 , 10 Ω for R 2 , and 5 Ω for R 3 in equation (1) to find R a . R a = ( 20 Ω ) ( 10 Ω ) + ( 10 Ω ) ( 5 Ω ) + ( 5 Ω ) ( 20 Ω ) 20 Ω = ( 200 + 50 + 100 ) Ω 2 20 Ω = 350 Ω 2 20 Ω = 17.5 Ω Substitute 20 Ω for R 1 , 10 Ω for R 2 , and 5 Ω for R 3 in equation (2) to find R b . R b = ( 20 Ω ) ( 10 Ω ) + ( 10 Ω ) ( 5 Ω ) + ( 5 Ω ) ( 20 Ω ) 10 Ω = ( 200 + 50 + 100 ) Ω 2 10 Ω = 350 Ω 2 10 Ω = 35 Ω Substitute 20 Ω for R 1 , 10 Ω for R 2 , and 5 Ω for R 3 in equation (3) to find R c . R c = ( 20 Ω ) ( 10 Ω ) + ( 10 Ω ) ( 5 Ω ) + ( 5 Ω ) ( 20 Ω ) 5 Ω = ( 200 + 50 + 100 ) Ω 2 5 Ω = 350 Ω 2 5 Ω = 70 Ω The transformed circuit from Y-to-Δ is shown in Figure 2

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ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Chapter 3.7, Problem 8AP

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Calculate the value of voltage v in the given circuit using Y-to-Δ transformation.

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Electric Circuits. (11th Edition)

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 - For each of the circuits shown in Fig. P...Ch. 3 - Prob. 2P

Ch. 3 - Prob. 3P Ch. 3 - Prob. 4P Ch. 3 - Prob. 5P Ch. 3 - Prob. 6P Ch. 3 - In the circuits in Fig. P 3.7(a)–(d), find the...Ch. 3 - Prob. 8P Ch. 3 - Find the power dissipated in each resistor in the...Ch. 3 - In the voltage-divider circuit shown in Fig. P...Ch. 3 - Calculate the no-load voltage υo for the...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 - The voltage divider in Fig. P3.16 (a) is loaded...Ch. 3 - There is often a need to produce more than one...Ch. 3 - For the current-divider circuit in Fig. P3.19...Ch. 3 - Find the power dissipated in the 30 resistor in...Ch. 3 - Specify the resistors in the current-divider...Ch. 3 - Show that the current in the kth branch of the...Ch. 3 - Look at the circuit in Fig. P3.1 (a). Use voltage...Ch. 3 - Look at the circuit in Fig. P3.1 (d). Use current...Ch. 3 - Attach a 6 V voltage source between the terminals...Ch. 3 - Look at the circuit in Fig. P3.7(a). Use current...Ch. 3 - Prob. 27P Ch. 3 - Prob. 28P Ch. 3 - For the circuit in Fig. P3.29, calculate i1 and i2...Ch. 3 - Find υ1 and υ2 in the circuit in Fig. P3.30 using...Ch. 3 - Find υo in the circuit in Fig. P3.31 using voltage...Ch. 3 - Find the voltage υx in the circuit in Fig. P3.32...Ch. 3 - A shunt resistor and a 50 mV. 1 mA d’Arsonval...Ch. 3 - Show for the ammeter circuit in Fig. P3.34 that...Ch. 3 - A d'Arsonval ammeter is shown in Fig....Ch. 3 - A d'Arsonval movement is rated at 2 mA and 100 mV....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 - The voltmeter shown in Fig. P3.42 (a) has a...Ch. 3 - Assume in designing the multirange voltmeter shown...Ch. 3 - The voltage-divider circuit shown in Fig. P3.44 is...Ch. 3 - Prob. 45P Ch. 3 - You have been told that the dc voltage of a power...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 - The bridge circuit shown in Fig. 3.28 is energized...Ch. 3 - Find the detector current id in the unbalanced...Ch. 3 - Find the power dissipated in the 18Ω resistor in...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 - Use a Δ-to-Y transformation to find the voltages...Ch. 3 - Prob. 59P Ch. 3 - Find io and the power dissipated in the 140Ω...Ch. 3 - Find the equivalent resistance Rab in the circuit...Ch. 3 - Find the resistance seen by the ideal voltage...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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