Sinusoidal Steady-State Analysis

In the context of sinusoidal steady-state analysis, what is the term for the abbreviated complex representation of a real sinusoidal current or voltage, which contains only amplitude and phase information?

What is the correct phasor representation V for the time-domain voltage v(t) = 100 cos(400t - 30 degrees) volts?

For a sinusoidal steady-state circuit, what is the relationship between the phasor voltage V across an inductor and the phasor current I through it?

What is the correct phasor relationship between the current I and voltage V for a capacitor in a sinusoidal steady-state circuit?

A sinusoidal voltage source vs(t) = 40 cos(8000t) V is applied to a series RL circuit. The resulting steady-state current is measured. According to Practice problem 10.3, what is the value of the inductor voltage, vL, at t = 0?

What are the three mandatory conditions that must be met to compare the phase relationship between two sinusoidal waves?

Find the angle by which the current i1 = 1.4 sin(120 pi t - 70 degrees) A lags the voltage v1 = 120 cos(120 pi t - 40 degrees) V.

In the frequency domain, what is the definition of impedance (Z)?

What is the correct relationship between admittance (Y), conductance (G), and susceptance (B)?

A 5 mH inductor is in series with a 100 microFarad capacitor. What is the equivalent impedance of this combination at a frequency of omega = 10,000 rad/s?

What is the equivalent impedance of the parallel combination of a 5 mH inductor and a 100 microFarad capacitor at an operating frequency of omega = 10,000 rad/s?

A circuit consists of a 1000 ohm resistor in series with a 1 mF capacitor. What is the equivalent impedance of the circuit at an operating frequency of 20 rad/s?

In a frequency-domain circuit with two nodes V1 and V2, the KCL equation at node V1 is (0.2 + j0.2)V1 - j0.1V2 = 1. The KCL equation at node V2 is -j0.1V1 + (0.1 - j0.1)V2 = j0.5. What is the phasor voltage V1?

A frequency-domain circuit is analyzed using mesh analysis, yielding the equations: (3 + j4)I1 - j4I2 = 10 and (2 - j4)I1 + j2I2 = 0. What is the value of the phasor mesh current I2?

When analyzing a linear circuit with multiple sinusoidal sources operating at different frequencies, what analysis technique must be used?

Find the Thévenin equivalent impedance Zth seen by the -j10 ohm impedance in the circuit described in Example 10.11.

In a phasor diagram for a series RLC circuit, if the current phasor I is used as the reference (along the positive real axis), how would the voltage phasor for the inductor, VL, be oriented?

The primary advantage of using the complex forcing function method to solve for the sinusoidal steady-state response is that it transforms the circuit's governing equation from what to what?

What is the inductive reactance of a 30 mH inductor at a frequency of 1000 rad/s?

What is the impedance of a 2 pF capacitor at an operating frequency of ω = 3000 rad/s?

Transform the time-domain current i(t) = -5 sin(580t - 110 degrees) A into its standard cosine-based phasor form.

Given the phasor current I = 20 + j10 A, and an operating frequency of omega = 2000 rad/s, what is the instantaneous value of the current at t = 1 ms?

A sinusoidal voltage of 8 / -50 degrees V at a frequency of 100 rad/s is applied to a 4 H inductor. What is the resulting phasor current?

For a simple RC circuit with a complex source of 3e^(j5t) V, a 1 ohm resistor, and a 2 F capacitor, the resulting steady-state capacitor voltage is found to be 29.85 cos(5t - 84.3 degrees) mV. What was the complex phasor Vm for the capacitor voltage?

In the frequency-domain circuit of Figure 10.21, with a source of 100/0 degrees V, a resistor -j5 ohms, a resistor 5 ohms, and an inductor j5 ohms, what is the phasor current I1?

What is the equivalent impedance Zeq for the circuit in Example 10.7, which has a 1.5 kOhm resistor in series with the parallel combination of a 1 kOhm resistor and an inductor with impedance j1 kOhm, and a capacitor with impedance -j2 kOhm?

A circuit has a source vs(t) = 40 sin(3000t) V. What is the correct phasor representation Vs to use for frequency-domain analysis?

In a linear circuit, a sinusoidal forcing function Vm cos(ωt + θ) produces a steady-state response Im cos(ωt + φ). If the forcing function is changed to jVm sin(ωt + θ), what is the resulting response?

The steady-state response of a circuit is found by assuming a solution composed of the forcing function plus what other functions?

A series RL circuit with R=20 ohms and L=30 mH is driven by a voltage source vs = 8 cos(1000t) V. What is the steady-state current iL(t)?

How does Kirchhoff's Voltage Law (KVL) apply to phasors in the frequency domain?

In the RLC circuit of Example 10.5, two sources operate at omega = 2 rad/s. The capacitor current is Ic = 2 / 28 degrees A. What is the voltage Vc across the capacitor, which has an impedance of -j/2 ohms?

What is the key difference between analyzing a resistive circuit with a sinusoidal source versus analyzing an RL or RC circuit with a sinusoidal source using time-domain differential equations?

The term 'steady-state response' in the context of sinusoidal sources refers to what condition?

A circuit contains two sinusoidal sources: one at 3 cos(5t) A and another at 2 cos(3t) A. To find the power dissipated by a 10 ohm resistor in the circuit, what is the correct procedure?

The resistive component of an impedance Z = R + jX is 8 ohms, but it is part of a parallel RL circuit. Is the resistance of the physical resistor in the circuit necessarily 8 ohms?

A complex current 4e^(j800t) A is applied to the series combination of a 1 mF capacitor and a 2 ohm resistor. What is the resulting complex voltage?

What is the equivalent admittance Yeq for a circuit with impedance Zeq = 2 + j1.5 kOhms?

In a parallel RC circuit with a single voltage V across both components, what is the relationship between the capacitor current phasor Ic and the resistor current phasor Ir in a phasor diagram?

If a time domain voltage is v(t) = 115 sin(500t + 45 degrees) volts, what is the correct representation using a cosine function?

A sinusoidal forcing function is described by Vm cos(ωt). The forced response in a series RL circuit is found to be I(t) = A cos(ωt - θ). What is the expression for the amplitude A?

For the frequency-domain circuit in Practice 10.12, what is the node voltage V1?

In the analysis of the high-frequency hybrid-pi transistor model in Section 10.7, why does the amplifier gain decrease as frequency increases?

A complex number is given as (2-j7)/(3-j). What is its representation in polar form?

An RLC circuit has a source that provides a voltage of 10 cos(1000t) V. The circuit has a 3 ohm resistor, a 4 mH inductor, and a capacitor. The circuit also contains a dependent source of 2*I1. The mesh equations are (3+j4)I1 - j4I2 = 10 and (2-j4)I1 + j2I2 = 0. What is the time-domain expression for the current i1(t)?

In a phasor diagram, if the voltage phasor V is 1/0 degrees and the current phasor I is 0.2 + j0.1 A, what is the geometric relationship between them?

What is the primary reason for using a double-headed arrow to indicate mutual coupling between two coils in a circuit diagram?

If two sinusoidal voltages are v1 = 120 cos(120 pi t - 40 degrees) V and v2 = -0.8 cos(120 pi t - 110 degrees) A, what is the angle by which i1 (v2) lags v1?

For an RLC circuit with a source vs(t) operating at 40 sin(3000t) V, a 1.5 kOhm resistor, an inductor with impedance j1 kOhm and a capacitor with impedance -j2 kOhm, what is the phasor current I?

A general sinusoidal current i(t) = Im cos(ωt + φ) is transformed into a phasor I by a series of steps. Which of the following correctly describes the final step of the transformation?