Capacitors and Inductors

What is the fundamental relationship defining the current, i, flowing through a capacitor with capacitance, C, in terms of the voltage, v, across it?

How does an ideal capacitor behave in a circuit when subjected to a constant DC voltage?

A 10 mF capacitor has a voltage across it given by v(t) = 5e^(-2t) V. What is the current i(t) flowing through it?

What is the formula for the energy, wC, stored in an ideal capacitor with capacitance C and voltage v across its terminals?

Calculate the energy stored in a 500 microfarad capacitor when the voltage across it is 10 V.

What is the defining voltage-current relationship for an ideal inductor with inductance, L, in terms of the current, i, flowing through it?

How does an ideal inductor behave in a circuit when subjected to a constant DC current?

The current through a 200 mH inductor is iL(t) = 4e^(-t) A. What is the voltage vL(t) across the inductor?

What is the formula for the energy, wL, stored in an ideal inductor with inductance L and current i flowing through it?

Calculate the energy stored in a 3 H inductor when a current of 2 A is flowing through it.

What is one of the key characteristics of an ideal capacitor regarding instantaneous voltage changes?

What is a key characteristic of an ideal inductor concerning instantaneous current changes?

How is the equivalent inductance, Leq, of N inductors connected in series calculated?

How do N capacitors connected in parallel combine to form an equivalent capacitance, Ceq?

A 6 microfarad capacitor and a 3 microfarad capacitor are connected in series. What is their equivalent capacitance?

Two inductors, one 3 H and one 6 H, are connected in parallel. What is their equivalent inductance?

In the context of the four fundamental circuit variables (charge q, current i, voltage v, flux linkage phi), which passive element provides a direct relationship between charge q and voltage v?

What function does an ideal op-amp circuit perform if a capacitor is used as the feedback element and a resistor is connected to the inverting input?

For the ideal op-amp integrator circuit with input resistor R1 = 100 k-ohm and feedback capacitor Cf = 500 microfarad, what is the output voltage if the input is vs = 20 sin(540t) mV and the initial capacitor voltage is zero?

What function does an ideal op-amp circuit perform if a capacitor is connected to the inverting input from the source, and a resistor is used as the feedback element?

For an ideal op-amp differentiator with input capacitor C1 = 1 microfarad and feedback resistor Rf = 500 k-ohm, what is the output voltage if the input is vs(t) = 2t V?

According to the principle of duality as applied to circuit elements, what is the dual of an inductor?

If a series RL circuit is considered, what is its dual network?

In a source-free parallel RLC circuit with R = 6 ohms, L = 7 H, and C = 1/42 F, the initial voltage v(0) is 0 V and the initial inductor current i(0) is 10 A. What is the value of the capacitor current, iC, at t=0?

What is the physical unit of capacitance, the farad (F), defined as?

What is the physical unit of inductance, the henry (H), defined as?

A 12 H inductor and an 8 H inductor are connected in series. What is their total equivalent inductance?

A 12 microfarad capacitor and an 8 microfarad capacitor are connected in parallel. What is their total equivalent capacitance?

The voltage across a 2.5 F capacitor is v(t) = 0 for t < 1s, and v(t) = 8(t-1) V for t >= 1s. What is the current flowing through the capacitor at t = 3s?

Which of the following statements about ideal capacitors and inductors is true regarding energy dissipation?

The voltage across a 5 H inductor is 10 V for the interval 0 < t < 2 s, and 0 V otherwise. If the initial current i(0) is 0 A, what is the inductor current at t = 2 s?

Three capacitors with values 2 F, 3 F, and 6 F are connected in series. What is the equivalent capacitance?

Three inductors with values 2 H, 3 H, and 6 H are connected in parallel. What is the equivalent inductance?

What physical phenomenon, hypothesized by James Clerk Maxwell, allows Kirchhoff's current law to hold for a capacitor, explaining how current seems to flow 'through' it?

What is the primary attribute of an ideal current source as described in the context of op-amp circuits?

The voltage across a 100 pF capacitor is given by the waveform in Figure 7.6. The voltage is 0 for t < 1 ms and ramps linearly to 2 V at t = 2 ms, after which it is constant. What is the current through the capacitor between 1 ms and 2 ms?

The current through a 25 mH inductor is given by iL = 8(1 - e^(-40t)) mA. What is the power being delivered to the inductor at t = 50 ms?

A 1 H, 3 H, and 5 H inductor are in series, and this combination is in parallel with a 9 H inductor. What is the equivalent inductance of the entire network?

A 10 F and a 15 F capacitor are in parallel. This combination is in series with a 5 F capacitor. What is the equivalent capacitance of the network?

Why might a circuit designer prefer to use a capacitor-based op-amp circuit (like a differentiator) instead of an inductor-based one to achieve the same function?

An RLC circuit is an example of a linear circuit. What principle, as a result of this linearity, can be applied to simplify analysis when multiple sources are present?

What is the integral relationship for the voltage v(t) across a capacitor with capacitance C, in terms of its current i(t) and initial voltage v(t0)?

What is the integral relationship for the current i(t) through an inductor with inductance L, in terms of the voltage v(t) across it and initial current i(t0)?

A 137 pF capacitor is connected to a voltage source such that vC(t) = 12 V for t < 0 and vC(t) = 12e^(-2t) V for t >= 0. What is the energy stored in the capacitor at t=0?

An 8 pH inductor has a current of 4e^(-t) A. What is the voltage across it at t=0?

In the circuit of Fig 7.28, which shows an op-amp differentiator, what is the expression for the output voltage, vout, in terms of the source voltage, vs?

For the op-amp circuit in Figure 7.29, which has an inductor Lf in the feedback path and a resistor R1 at the input, what is the expression for the output voltage vout in terms of the source voltage vs?