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Problem 3: Consider two circuits coupled together by a transformer. The primary circuit is driven by an ac voltage source V(t) = Vo coswt in series with a resistor Ri and an inductor consisting of a long solenoid with length l, cross sectional area A, and N1 turns of insulated wire wrapped around a core having linear permeability u. The secondary circuit consists of a resistor R, in a closed loop. The secondary circuit is in "magnetic contact" with the primary circuit, in the sense that the wire in the secondary circuit is wrapped N2 times around the same solenoidal core. The total magnetic field inside the solenoid is the sum B1+B2, where B1 is the field produced by the current I in the primary, and B2 is the field produced by the current I in the secondary. (a) Writé down an expression for B1 in terms of I1. Write down an expression for B2 in terms of I2. (b) The extended Kirchoff voltage law for the primary circuit is V(t)-IR1 = 01 where 1 secondary circuit is -I R2 = 2 where 2 = (B1 +B2)N2A. Combine these equations and eliminate (B1+B2), so as to show that V(t)-R1 = -h R2. (c) Suppose that the voltage dropped across your house is I R2, and that V(t)-IR1 is the voltage in the transmission lines in your neighborhood. What %3D (B1 + B2)N1A. The extended Kirchoff voltage law for the

Problem 3: Consider two circuits coupled together by a transformer. The primary circuit is driven by an ac voltage source V(t) = Vo coswt in series with a resistor Ri and an inductor consisting of a long solenoid with length l, cross sectional area A, and N1 turns of insulated wire wrapped around a core having linear permeability u. The secondary circuit consists of a resistor R, in a closed loop. The secondary circuit is in "magnetic contact" with the primary circuit, in the sense that the wire in the secondary circuit is wrapped N2 times around the same solenoidal core. The total magnetic field inside the solenoid is the sum B1+B2, where B1 is the field produced by the current I in the primary, and B2 is the field produced by the current I in the secondary. (a) Writé down an expression for B1 in terms of I1. Write down an expression for B2 in terms of I2. (b) The extended Kirchoff voltage law for the primary circuit is V(t)-IR1 = 01 where 1 secondary circuit is -I R2 = 2 where 2 = (B1 +B2)N2A. Combine these equations and eliminate (B1+B2), so as to show that V(t)-R1 = -h R2. (c) Suppose that the voltage dropped across your house is I R2, and that V(t)-IR1 is the voltage in the transmission lines in your neighborhood. What %3D (B1 + B2)N1A. The extended Kirchoff voltage law for the

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Problem 3: Consider two circuits coupled together by a transformer. The primary circuit is driven by an ac voltage source Vt) = Vo coswt in series with a resistor R1 and an inductor consisting of a long solenoid with length l, cross sectional area A, and N1 turns of insulated wire wrapped around a core having linear permeability u. The secondary circuit consists of a resistor R, in a closed loop. The secondary circuit is in "magnetic contact" with the primary circuit, in the sense that the wire in the secondary circuit is wrapped N, times around the same solenoidal core. The total magnetic field inside the solenoid is the sum B1+B2, where B1 is the field produced by the current I, in the primary, and B2 is the field produced by the current I in the secondary. (a) Writé down an expression for B1 in terms of I1. Write down an expression for B2 in terms of I2. (b) The extended Kirchoff voltage law for the primary circuit is V(t)-IR1 = 1 where 1 secondary circuit is -I R2 = , where 2 = (B1+ B2)N2A. Combine these equations and eliminate (B1+B2), so as to show that V(t)-IR1 = -, R2. (c) Suppose that the voltage dropped across your house is I R2, and that V(t)-IR1 is the voltage in the transmission lines in your neighborhood. What (B1 +B2)N14. The extended Kirchoff voltage law for the
Transcribed Image Text:Problem 3: Consider two circuits coupled together by a transformer. The primary circuit is driven by an ac voltage source Vt) = Vo coswt in series with a resistor R1 and an inductor consisting of a long solenoid with length l, cross sectional area A, and N1 turns of insulated wire wrapped around a core having linear permeability u. The secondary circuit consists of a resistor R, in a closed loop. The secondary circuit is in "magnetic contact" with the primary circuit, in the sense that the wire in the secondary circuit is wrapped N, times around the same solenoidal core. The total magnetic field inside the solenoid is the sum B1+B2, where B1 is the field produced by the current I, in the primary, and B2 is the field produced by the current I in the secondary. (a) Writé down an expression for B1 in terms of I1. Write down an expression for B2 in terms of I2. (b) The extended Kirchoff voltage law for the primary circuit is V(t)-IR1 = 1 where 1 secondary circuit is -I R2 = , where 2 = (B1+ B2)N2A. Combine these equations and eliminate (B1+B2), so as to show that V(t)-IR1 = -, R2. (c) Suppose that the voltage dropped across your house is I R2, and that V(t)-IR1 is the voltage in the transmission lines in your neighborhood. What (B1 +B2)N14. The extended Kirchoff voltage law for the
should the turns ratio N2/N1 be so that 13,000 volts RMS in the transmission line is converted down to 240 volts RMS? v) V, cascwt) R. priman 下 ATR
Transcribed Image Text:should the turns ratio N2/N1 be so that 13,000 volts RMS in the transmission line is converted down to 240 volts RMS? v) V, cascwt) R. priman 下 ATR
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