Basic RL and RC Circuits

In a source-free series RL circuit, the current i(t) is described by the equation i(t) = I0 * e^(-Rt/L). If the initial current I0 is 2 A, the resistance R is 200 ohms, and the inductance L is 50 mH, what is the inductor current iL at t = 200 microseconds?

What is the correct definition of the 'natural response' of a circuit?

In a DC circuit that has been connected for a very long time, how does an ideal inductor behave?

In a DC circuit that has been operating for a long time, how does an ideal capacitor behave?

What is the time constant (τ) for a source-free parallel RC circuit consisting of a 10-kohm resistor and a 2-microfarad capacitor?

The unit-step function u(t - t0) is a singularity function used to model switching events. What are its defined values?

A series RL circuit is driven by a voltage step source of 12u(t-3) V. The resistance is 1 kohm and the inductance is 50 mH. What is the forced response for the current, i(infinity)?

Which rule governs the behavior of an inductor's current at the instant a switch is thrown in a circuit?

Which rule governs the behavior of a capacitor's voltage at the instant a switch is thrown in a circuit?

A series RL circuit with R=200 ohms and L=4 H is driven by a voltage source vs = 20u(t) V. What is the magnitude of the inductor current at t = 15 ms?

What is the formula for the energy stored in an ideal inductor L with a current i flowing through it?

What is the formula for the energy stored in an ideal capacitor C with a voltage v across it?

After a transient event in a source-free RL or RC circuit, approximately how many time constants are considered sufficient for the transient response to become negligible (less than 1 percent of its initial value)?

How can a rectangular voltage pulse of amplitude V0, starting at t = t0 and ending at t = t1, be represented using unit-step functions?

In a source-free circuit with multiple inductors and resistors, what is the time constant τ if the inductors can be combined into an equivalent inductance Leq and the resistors into an equivalent resistance Req seen by the inductor?

For a source-free RC circuit with an initial voltage V0=9 V, resistance R=6 ohms, and capacitance C=10 microfarads, what is the capacitor voltage at t = 200 microseconds?

In the context of sequentially switched circuits, what is the primary consequence if the circuit's time constant τ is much larger than the pulse width Wp?

The complete response of a driven RL or RC circuit is the sum of two components. What are they?

What is the characteristic equation for a source-free series RL circuit described by the differential equation L(di/dt) + Ri = 0?

What is the form of a critically damped response for a second-order circuit like an RLC circuit?

For a source-free series RL circuit, what happens to the current after one time constant has passed (t = τ)?

How is the time constant of a more general RL or RC circuit containing multiple resistors found when there is only one energy storage element?

The voltage source in a circuit is given by vs = 60 - 40u(t) V. What is the value of this source at t=0- (just before t=0)?

The voltage source in a circuit is given by vs = 60 - 40u(t) V. What is the value of this source at t=0+ (just after t=0)?

What is the primary factor that determines whether an RC circuit subjected to a pulse train has time to fully discharge between pulses?

A source-free RC circuit with a dependent source has a calculated Thévenin equivalent resistance of -60 ohms and a capacitance of 1 microfarad. What is the nature of this circuit's response?

What is the general expression for the current i(t) in a driven RL circuit, combining the forced response (if) and the natural response, where K is the unknown constant?

What is the final value (as t approaches infinity) of the inductor current in the circuit of Example 8.8, where the loop is driven by a 100V DC source and has a total resistance of 2 ohms?

In the circuit of Example 8.8, the inductor current for t>0 is i(t) = 50 - 25e^(-0.5t) A. The initial current i(0-) was 25 A. What does the natural response term, -25e^(-0.5t), physically represent?

A rectangular voltage pulse is applied to a series RL circuit. The pulse has an amplitude of V0 and duration t0. The response current during the pulse (0 < t < t0) is i(t) = (V0/R) * (1 - e^(-Rt/L)). What is the expression for the current for t > t0, after the pulse ends?

In the summary of the procedure for analyzing a driven RC circuit, what is the expression for the total response f(t) in terms of the final value f(infinity) and the initial value f(0+)?

An RC circuit has an equivalent resistance of 14.7 ohms and a capacitance of 22 microfarads. What is its time constant τ?

In the Practical Application section discussing digital circuits, the interconnect pathway between two logic gates is modeled as what type of simple circuit?

According to the Practical Application section, if an interconnect pathway has an RC time constant of 50 picoseconds, what is the maximum operating frequency, f_max?

The response of a first-order circuit is `v(t) = V0 * e^(-t/τ)`. At what time `t` will the response decay to exactly half of its initial value?

In a source-free series RL circuit, if the resistance R is doubled while the inductance L remains constant, what happens to the time constant τ?

In a source-free parallel RC circuit, if the capacitance C is halved while the resistance R remains constant, what happens to the time constant τ?

Which of the following best describes the term 'forced response' in a circuit?

A source-free RL circuit has an initial current of 6 A, a resistance of 1 kohm, and an inductance of 500 nH. What is the current through the resistor at t = 1 nanosecond?

What is the primary reason that RC circuits are often more common in integrated circuits than RL circuits?

In a driven RC circuit, how is the constant for the natural response term (A) determined?

The concept of duality relates the behavior of RL and RC circuits. If an RL circuit has R = 10 ohms and L = 5 H, what are the component values for its exact dual RC circuit?

The voltage across a 40-ohm resistor in a source-free RL circuit is v(t). At t=0+, the inductor current iL(0+) is -2.4 A, and the current flows from the negative to the positive terminal of the resistor voltage definition. What is v(0+)?

The circuit in Figure 8.22a consists of a capacitor C in series with resistor R1, and this combination is in parallel with resistor R2. This whole group is in series with resistor R3. How is the equivalent resistance seen by the capacitor calculated?

How is the initial rate of decay of current in a source-free RL circuit related to the time constant τ?

In a source-free RC circuit with voltage v(t), the total energy dissipated in the resistor from t=0 to t=infinity is equal to what quantity?

If a source-free RL circuit has a time constant of 0.5 seconds, how long does it take for the inductor current to decay to approximately 1.8 percent of its initial value?

What is the primary characteristic of the response of an RC circuit to a series of pulses when the time between pulses is much shorter than the time constant τ?

An RC circuit is constructed with a 2-ohm and 4-ohm resistor in series with a 10-microfarad capacitor. If the circuit is source-free and has an initial capacitor voltage of 9V, what is the time constant?

In a driven RL circuit with a DC source, the total current can be written as i(t) = i(infinity) + [i(0+) - i(infinity)] * e^(-t/τ). What does the term i(infinity) represent?