Consider the following transformer circuit assuming an ideal transformer. In this circuit the signal generator will provide a 10-Volt peak-to-peak sinusoidal signal at a frequency of 1.0 kHz. Assume that L₁ = 0.65 H, L2 = 0.00492 H (=4.92 mH) and that the coupling constant = 0.99925. VG1 + R1 1k N1:N2 11.5:1 12 + + V1 N1 N2 V2 R2 8.2 1) Find the following using the theory presented in the prelab reading: a) Start with Equations (2) of the prelab reading and show that the input impedance to an ideal transformer is given by the equation for Z1 (= V₁/I1) in Equations (4) of the prelab reading. Equations (2) are: V₁ = j@L₁I₁ +j@MI2 and V₂ = j@MI₁ +j@L₂I 2 The equation for the input impedance is: Z1 = = = jwL₁ + 11 (WM)² jwL2+ZL b) Assuming that ZL is a real impedance, find the equations for the real and imaginary parts of Z1. c) Use your equations from part (b) to calculate the value of the input impedance (Z1) at an operating frequency of 200 Hz. Assume that the load impedance is 8.2 Ohms (characteristic of an audio speaker) and completely real. Find both the real and imaginary parts of Z1. d) Repeat part (c) at an operating frequency of 5 kHz e) Calculate the voltages V1 and V2 at 5 kHz f) Calculate the currents 11 and 12 at 5 kHz g) Calculate the amount of power supplied by the signal generator, VG1, and the amount of power dissipated in each of the two resistors in the circuit at 5 kHz.
Consider the following transformer circuit assuming an ideal transformer. In this circuit the signal generator will provide a 10-Volt peak-to-peak sinusoidal signal at a frequency of 1.0 kHz. Assume that L₁ = 0.65 H, L2 = 0.00492 H (=4.92 mH) and that the coupling constant = 0.99925. VG1 + R1 1k N1:N2 11.5:1 12 + + V1 N1 N2 V2 R2 8.2 1) Find the following using the theory presented in the prelab reading: a) Start with Equations (2) of the prelab reading and show that the input impedance to an ideal transformer is given by the equation for Z1 (= V₁/I1) in Equations (4) of the prelab reading. Equations (2) are: V₁ = j@L₁I₁ +j@MI2 and V₂ = j@MI₁ +j@L₂I 2 The equation for the input impedance is: Z1 = = = jwL₁ + 11 (WM)² jwL2+ZL b) Assuming that ZL is a real impedance, find the equations for the real and imaginary parts of Z1. c) Use your equations from part (b) to calculate the value of the input impedance (Z1) at an operating frequency of 200 Hz. Assume that the load impedance is 8.2 Ohms (characteristic of an audio speaker) and completely real. Find both the real and imaginary parts of Z1. d) Repeat part (c) at an operating frequency of 5 kHz e) Calculate the voltages V1 and V2 at 5 kHz f) Calculate the currents 11 and 12 at 5 kHz g) Calculate the amount of power supplied by the signal generator, VG1, and the amount of power dissipated in each of the two resistors in the circuit at 5 kHz.
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Transcribed Image Text:Consider the following transformer circuit assuming an ideal transformer. In this circuit
the signal generator will provide a 10-Volt peak-to-peak sinusoidal signal at a frequency
of 1.0 kHz. Assume that L₁ = 0.65 H, L2 = 0.00492 H (=4.92 mH) and that the coupling
constant <k> = 0.99925.
VG1
+
R1 1k
N1:N2
11.5:1
12
+
+
V1 N1
N2
V2
R2 8.2
1) Find the following using the theory presented in the prelab reading:
a) Start with Equations (2) of the prelab reading and show that the input impedance
to an ideal transformer is given by the equation for Z1 (= V₁/I1) in Equations (4) of
the prelab reading.
Equations (2) are: V₁ = j@L₁I₁ +j@MI2 and V₂ = j@MI₁ +j@L₂I 2
The equation for the input impedance is: Z1 =
=
= jwL₁ +
11
(WM)²
jwL2+ZL
b) Assuming that ZL is a real impedance, find the equations for the real and
imaginary parts of Z1.
c) Use your equations from part (b) to calculate the value of the input impedance
(Z1) at an operating frequency of 200 Hz. Assume that the load impedance is 8.2
Ohms (characteristic of an audio speaker) and completely real. Find both the real
and imaginary parts of Z1.
d) Repeat part (c) at an operating frequency of 5 kHz
e) Calculate the voltages V1 and V2 at 5 kHz
f) Calculate the currents 11 and 12 at 5 kHz
g) Calculate the amount of power supplied by the signal generator, VG1, and the
amount of power dissipated in each of the two resistors in the circuit at 5 kHz.
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