Question 49 of 50

In the context of a discharging capacitance through a resistance, the solution for the capacitor voltage is anticipated to be an exponential of the form vC(t) = Kest. What does this assumption stem from?

For a first-order RC circuit with R = 2 M-ohm and C = 3 mF, what is the time constant τ?

In a first-order circuit, what is the key difference between the transient response and the steady-state response?

How do ideal capacitors and inductors behave under DC steady-state conditions?

What is the steady-state current, ix, in the circuit of Figure 4.6(a) for t >> 0, given R1 = 5 ohm and R2 = 5 ohm, connected to a 10 V source?

What is the time constant for an RL circuit?

In the RL Transient Analysis of Example 4.4, with Vs = 100 V, R = 50 ohm, and L = 0.1 H, what is the steady-state current after the switch is closed?

What is the general form of the solution for a variable x(t) in a first-order differential equation for an RC or RL circuit with a general source?

In a second-order RLC circuit, what defines the undamped resonant frequency, ω₀?

For a second-order RLC circuit, what is the condition for the system to be critically damped?

What is the form of the complementary solution xc(t) for an underdamped (ζ < 1) second-order circuit?

In the analysis of a series RLC circuit in Example 4.7, with R = 300 ohm, L = 10 mH, and C = 1 μF, what is the value of the damping ratio ζ?

What physical phenomena in a second-order system's step response are referred to as 'overshoot' and 'ringing'?

How does the formula for the damping coefficient α differ between a series RLC circuit and a parallel RLC circuit?

According to the step-by-step process for using the MATLAB Symbolic Toolbox for transient analysis, what must be done after writing the differential-integral equations for the circuit variables?

Why must the voltage across a capacitor be continuous in a circuit where the current is finite?

In a discharging RC circuit, after one time constant (t = τ), the capacitor voltage decays by what factor from its initial value?

In Example 4.2, with a Thévenin equivalent circuit of Vs = 5 V and R = 33.3 ohm charging a 3 μF capacitor, what is the time constant?

Why must the current through an inductor be continuous in a circuit where the voltage is finite?

In a charging RC circuit starting from zero initial voltage, after one time constant, the capacitor voltage reaches what percentage of its final value?

What is the primary limitation on the processing speed of digital computers, as discussed in the context of RC transients?

In the general solution of a first-order differential equation, which part of the solution is also known as the natural response?

When analyzing a circuit with a sinusoidal forcing function, such as in Example 4.6, what is the general form of the particular solution that is tried?

In Example 4.7, for the critically damped case with R = 200 ohm, what are the roots (s1, s2) of the characteristic equation?

How is the particular solution for a second-order circuit with a DC source typically found without solving the full differential equation?

What is the key characteristic of the solution to the homogeneous equation for a first-order circuit?

In Example 4.1, a circuit with R = 2 M-ohm and C = 3 microF has an initial voltage of 100 V. At what time tx does the voltage drop to 25 V?

For the series RLC circuit in Figure 4.21, the general second-order differential equation for the current i(t) is derived. How is the integrodifferential KVL equation converted to a pure differential equation?

What is the damping ratio ζ defined as in a second-order RLC circuit?

For a discharging RC circuit, how many time constants does it take for the capacitor voltage to be considered almost totally discharged for practical purposes?

What is the steady-state voltage, vx, in the circuit of Figure 4.6(a) for t >> 0, given R1 = 5 ohm, R2 = 5 ohm, and a 10 V source?

In the RL circuit of Example 4.5, after the switch opens at t=0, what is the time constant of the decaying current?

In a first-order circuit, which component determines the form of the particular solution?

What is the particular solution vCp(t) for the capacitor voltage in the series RLC circuit of Example 4.7, which is connected to a 10 V DC source at t=0?

For a second-order system, what are the roots of the characteristic equation in an overdamped case (ζ > 1)?

In Example 4.4, with R=50 ohm and L=0.1 H, what is the time constant τ of the RL circuit?

What is the value of the voltage across a charging capacitor at t=0+ if its voltage just before the switch closes, vC(0-), was 0 V?

In the MATLAB command `dsolve('DVL + 100*VL = -2000*sin(100*t)', 'VL(0) = 20')`, what do 'DVL' and 'VL(0) = 20' represent?

What are the steps for determining the forced response for RLC circuits with DC sources in steady state?

In Exercise 4.1, if R = 5000 ohm and C = 1 microF in a discharging circuit, at what time does the voltage reach 1 percent of its initial value?

What is the form of the characteristic equation for a second-order RLC circuit?

In Example 4.5, if Vs = 15 V, R1 = 10 ohm, R2 = 100 ohm, and L = 0.1 H, what is the maximum magnitude of the voltage v(t) across the inductor after the switch opens?

What is the physical significance of the 'natural frequency', ωn, in an underdamped second-order circuit?

For the parallel RLC circuit shown in Figure 4.31, what is the formula for the damping coefficient, α?

In Example 4.6, a first-order RC circuit is driven by a sinusoidal source. What is the time constant τ of this circuit, given R=5 k-ohm and C=1 microF?

In a series RLC circuit, if R = 100 ohm, L = 10 mH, and C = 1 μF, what is the natural frequency, ωn?

The response of a second-order system with a damping ratio of 0.1 will display which characteristic behavior?

What type of function is a 'unit step function', u(t)?

For the circuit in Example 4.9, what is the initial value of the capacitor current's rate of change, v'(0+)?