Markovic, Miroslav.D.: EEE161 Electromagnetics – Homework problems related to the Lab #1 1.1
Problem 1.1
In a series circuit comprised of AC source, Vs, and three different resistors, R1, R2, and R3, connected in series, as shown in Fig. 1.1, compute:
1.1.a.Equivalent resistance of these three resistors, Re;
1.1.b. Current flowing through them, IR, and
1.1.c. Voltage drop across all three resistors, VR1, VR2 and VR3.
1.1.d. In an arbitrary scale, draw the phasor diagram of voltage source and three voltage
drops by taking the voltage source as a reference phasor.
Solutions 1.0
1.1.a. The equivalent resistor, Re, of these three resistors is
(1.1)
1.1.b. According to the Ohm’s law, the current, IR, in the series circuit is
(1.2)
1.1.c. The voltage drops across the individual resistors,VR1, VR2 and VR3, are
(1.3)
(1.4)
and
(1.5)
respectively.
1.1.d. The phasor diagram of the voltage source and the voltage drops computed above is shown in
Fig. 1.1.1, but not to scale.
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Problem 1.2
In a series circuit comprised of AC source, Vs, whose frequency is f = 60 (Hz), two different resistors, R1 and R2, and two different inductances, L1 and L2, connected in series, as shown in Fig. 2.1, compute:
1.2.a. Equivalent resistance of these three resistors, Re;
1.2.b. Equivalent inductive reactance, XeL;
1.2.c. Complex impedance of this circuit, ZRL;
1.2.d. Current flowing through them, IRL;
1.2.e. Voltage drops across the resistors, VRe, and across the inductive inductances,
VL1 and VL2, and
1.2.f. Prove that the Kirchhoff’s voltage law is satisfied.
1.2.g. In an arbitrary scale, draw the phasor diagram of the voltage source and the three
voltagedrops across the resistors and inductors by taking the voltage source as
the reference phasor.
Solutions 1.2
1.2.a. The equivalent resistor, Re, of these three resistors is
(2.1)
1.2.b. The equivalent inductance, Le, of the two inductances connected in series is
(2.2)
and the corresponding inductive reactance, XeL, is
(2.3)
1.2.c. The complex impedance, ZRL, of this series circuit is
(2.4)
1.2.d. According to the Ohm’s law, the current, IRL, in the series circuit is
(2.5)
1.2.e.The voltage drop across the equivalent resistor,VRe, is
(2.6)
while the voltage drops across the individual inductances, VL1 and VL2, are
(2.7)
and
(2.8)
respectively.
1.2.f. According to the Kirchhoff’s voltage law, the algebraic sum of the voltage source and all voltage drops in this series circuit must be equal to zero, i.e.,
(2.9)
Note: Due to the rounding up errors done on a hand-held calculator, this result is not a perfect zero but acceptably close to it.
1.2.g. The phasor diagram of voltage source and voltage drops based on (2.5), (2.6), (2.7)and (2.8) are shown in Fig. 2.1.1, but not to scale.
***
Problem 1.3
In a series circuit comprised of AC source, Vs, whose frequency is f = 60 (Hz), one resistor, R, two different inductances, L1 and L2, and two capacitors, C1 and C2, connected in series, as shown in Fig. 3.1, compute:
1.3.a. Equivalent inductive reactance, XeL;
1.3.b. Equivalent capacitive reactance, XeC
1.3.c. Complex impedance of this circuit, ZRLC;
1.3.d. Current flowing through them, IRLC;
1.3.e. Voltage drops across the resistors, VR, and across the equivalent inductive
reactance,VLe;
1.3.f. Voltage drops across the individual capacitive reactances,VC1, and VC2, and
1.3.g. Prove that validity of the Kirchhoff’s voltage law.
1.3.h. In an arbitrary scale, draw the phasor diagram of voltage source and four voltage
drops across the resistor, and inductors and capacitors by taking the voltage source
as the reference phasor.
Solutions 1.3
1.3.a. The equivalent inductance, Le, of these two inductances connected in parallel is
(3.1)
and the corresponding equivalent inductive reactance, XeL, is
(3.2)
1.3.b. The equivalent capacitance, Ce, of these two capacitances connected in series is
(3.3)
and the corresponding equivalent capacitive reactance, Xec, is
(3.4)
1.3.c. The complex impedance, Z, of this series circuit is
(3.5)
1.3.d. According to the Ohm’s law, the current, IRLC, in the series circuit is
(3.6)
1.3.e. The voltage drop across the resistor,VR, is
(3.7)
while the voltage drops across the equivalent inductive reactance, VLe, is
(3.8)
1.3.f. The voltage drops across theindividual capacitive reactanceVXC1 and VXC2 are
(3.9)
and
(3.10)
1.3.g. According to the Kirchhoff’s voltage law, the algebraic sum of the voltage source and all voltage drops in this series circuit must be equal to zero, i.e.,
(3.11)
Note: Due to the rounding up errors done on a hand-held calculator, this result is not a perfect zero but acceptably close to it.
1.3.h. The phasor diagram of voltage source and voltage drops computed in (3.6) – (3.9) are shown in
Fig. 3.1.1, but not to scale.
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Note: The following three problems are designed to prepare students to the Lab #2
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