Electrical Circuits Quiz - Thevenin and Norton

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Questions and Answers

What is the equivalent resistance when a $50\Omega$, $40\Omega$, and $10\Omega$ resistor are in parallel?

The equivalent resistance cannot be calculated

$20\Omega$

$5\Omega$ (correct)

$4\Omega$

The Thevenin-Norton equivalent circuits are valid only for DC circuits.

False (B)

What type of sources can a circuit contain for Thevenin-Norton equivalent circuits to be valid?

dependent or independent

In the solution to AP 9.11, $V_{th}$ is determined using the principle of voltage division applied to the voltage across the 20 $\Omega$ resistor, which is equal to ______.

10Ix Signup and view all the answers

In AP 9.10, what method is utilized to find v0(t) when given $v_1 = 240\cos(4000t + 53.13^o)$ and $v_2 = 96\sin(4000t)$?

Source transformation (C) Signup and view all the answers

In the frequency domain, Kirchhoff's Voltage Law (KVL) states that the sum of all voltages around a closed loop equals a non-zero value.

False (B) Signup and view all the answers

Given a circuit with several sinusoidal currents, which of the following equations represents Kirchhoff's Current Law (KCL) in the frequency domain?

$I_1 + I_2 + I_3 + ... + I_n = 0$ (C) Signup and view all the answers

Which form of complex number representation is most suitable for performing multiplication and division?

Exponential form (A) Signup and view all the answers

In applying KVL in the frequency domain to a circuit with voltage sources $V_1$, $V_2$, and $V_3$, what equation must be satisfied?

$V_1 + V_2 + V_3 = 0$ Signup and view all the answers

Admittance is the reciprocal of impedance.

True (A) Signup and view all the answers

In the frequency domain, the application of KCL results in the sum of currents at a node being equal to ______.

zero Signup and view all the answers

What are the two equivalent circuits used to simplify complex circuits by reducing them to a voltage source and a series impedance or a current source and parallel admittance?

Thevenin and Norton Signup and view all the answers

What condition must be satisfied to transition from the instantaneous expression of KVL, $\Re {v_{m1} e^{j\theta_1} e^{j\omega t} + v_{m2} e^{j\theta_2} e^{j\omega t} + ... + v_{mn} e^{j\theta_n} e^{j\omega t} } = 0$, to its simplified frequency domain representation?

$e^{j \omega t} \neq 0$ (D) Signup and view all the answers

Match the following laws with their respective statements:

Kirchhoff's Voltage Law (KVL) = The sum of all voltages around any closed loop in a circuit is zero. Kirchhoff's Current Law (KCL) = The sum of all currents entering and exiting a node is zero. Signup and view all the answers

In sinusoidal circuits, the imaginary part of impedance is called ______.

reactance Signup and view all the answers

Match the circuit element with its corresponding impedance in sinusoidal circuits.

Resistor = R Inductor = $j\omega L$ Capacitor = $\frac{1}{j\omega C}$ Signup and view all the answers

Given $i_1 = 50 \cos(\omega t + 30^o)$ and $i_2 = 50 \cos(\omega t + 150^o)$ entering a node, which expression best describes KCL in the frequency domain for determining the current $i_3$ leaving the node?

$I_3 = -(50\angle 30^o + 50\angle 150^o)$ (D) Signup and view all the answers

When applying Kirchhoff's laws in the frequency domain, the frequency ($\omega$) must be the same for all sinusoidal sources involved.

True (A) Signup and view all the answers

In the context of circuit analysis, what is the primary purpose of applying a test voltage ($V_t$) when determining Thevenin impedance ($Z_{th}$)?

To calculate the equivalent resistance by finding the ratio of the test voltage to the resulting current ($V_t/I_x$) with independent sources disabled. (D) Signup and view all the answers

The node voltage method can only be applied to circuits operating in the time domain, and not to frequency domain circuits.

False (B) Signup and view all the answers

In mesh current analysis, what is the significance of solving for mesh currents ($I_1, I_2$, etc.)?

node voltages Signup and view all the answers

A phasor diagram visually represents the ______ and phase of quantities in the complex plane.

magnitude Signup and view all the answers

Match the circuit analysis method with its primary focus:

Node Voltage Method = Finding node voltages in a circuit Mesh Current Method = Finding loop currents in a circuit Phasor Diagrams = Visually representing magnitude and phase relationships Thevenin Impedance = Simplifying a circuit to an equivalent voltage source and series impedance Signup and view all the answers

In the given circuit, what condition must be met for the impedance angle ($\theta_Z$) to be equal to 45 degrees, allowing for the calculation of the capacitance (C)?

The real and imaginary parts of the impedance must be equal. (B) Signup and view all the answers

In a Delta-to-Wye transformation, each impedance in the Wye configuration is equal to the sum of the products of the impedances in the Delta configuration divided by the impedance that is opposite to the node being calculated.

False (B) Signup and view all the answers

If the voltage across an impedance is $V_s = 125 \angle -60^o$ and the resulting current has a phase angle of -105 degrees, what is the phase angle of the impedance?

45 degrees Signup and view all the answers

In the Delta-to-Wye transformation formulas, the Wye impedance $Z_1$ is calculated as $Z_1 = \frac{Z_b Z_c}{______}$.

Za + Zb + Zc Signup and view all the answers

What is the purpose of performing a Delta-to-Wye transformation on a circuit?

To simplify the circuit for easier analysis. (B) Signup and view all the answers

Match the following circuit parameters with their corresponding formulas in the context of the provided material:

Capacitance (C) = $C = \frac{1}{5000(160 - 90)}$ Impedance (Z) = $Z = 90 + j90$ Current (I) = $I = \frac{125}{127.28}$ Phase Angle of Impedance ($\theta_Z$) = $\theta_Z = 45^o$ Signup and view all the answers

When using Delta-to-Wye transformation to solve for current I, the initial Delta network is replaced by its equivalent Wye network to simplify the circuit before applying Ohm's Law or similar circuit analysis techniques.

True (A) Signup and view all the answers

Given $Z = 127.28 \angle 45^o$, and $V_s = 125 \angle -60^o$, calculate the magnitude of the current I.

0.982 A Signup and view all the answers

What is the phase relationship between voltage and current in a resistor?

Voltage and current are in phase. (D) Signup and view all the answers

The phasor representation of $v(t) = 10cos(\omega t + 30^o)$ is $V = 10\angle -30^o$.

False (B) Signup and view all the answers

If the current through a resistor is $i(t) = 2cos(\omega t)$, and the resistance is 5 ohms, what is the phasor representation of the voltage across the resistor?

10∠0° Signup and view all the answers

In the frequency domain, the voltage across an inductor is equal to ______ times the current through the inductor.

jωL Signup and view all the answers

Given a voltage phasor $V = 5\angle 90^o$ V across an inductor with inductance L = 2H at a frequency $\omega = 1$ rad/s, what is the current phasor?

$2.5\angle -90^o$ A (A) Signup and view all the answers

Which expression correctly relates voltage (V) and current (I) in a resistor within the frequency domain?

$V = RI$ (D) Signup and view all the answers

What does the term 'phasor' represent?

The peak amplitude and phase angle of a sinusoidal signal. (B) Signup and view all the answers

Match the time-domain expressions with their corresponding phasor representations.

$10cos(\omega t + 45^o)$ = $10\angle 45^o$ $5sin(\omega t)$ = $5\angle -90^o$ $2cos(\omega t - 30^o)$ = $2\angle -30^o$ $8sin(\omega t + 60^o)$ = $8\angle -30^o$ Signup and view all the answers

Signup and view all the answers

Flashcards

Kirchhoff's Voltage Law (KVL)

The sum of all voltages in a closed loop equals zero.

KVL in Frequency Domain

Voltage sum in frequency domain equals zero: V1 + V2 + ... + Vn = 0.