Inductance and Capacitance

In the context of a capacitor, what is the relationship between the stored charge q, the capacitance C, and the voltage v between the plates in an ideal capacitor?

What is the current i(t) flowing through a capacitor with capacitance C, as a function of the voltage v(t) across it, assuming the passive configuration?

How does an ideal capacitor behave in a circuit with a steady DC voltage after transients have settled?

Three capacitors with values C1, C2, and C3 are connected in parallel. What is the equivalent capacitance, Ceq, of this combination?

What is the equivalent capacitance for three capacitances connected in series?

A parallel-plate capacitor has rectangular plates of 10 cm by 20 cm, separated by an air dielectric with a thickness of 0.1 mm. The dielectric constant of vacuum is approximately 8.85 x 10^-12 F/m, and the relative dielectric constant for air is 1.00. What is the capacitance?

What is a key characteristic of electrolytic capacitors that distinguishes them from many other types, such as those with polyethylene or Mylar dielectrics?

A capacitor C1 is charged to 100 V and has a capacitance of 1 microfarad. It is then connected at t=0 to an uncharged capacitor C2, also of 1 microfarad. What is the total stored energy in the two capacitors after the switch is closed?

For an ideal inductor, what is the relationship between the voltage v(t) across it and the current i(t) flowing through it, assuming the passive reference configuration?

What is the formula for the energy w(t) stored in an inductor with inductance L and current i(t)?

A current through a 5 H inductance is shown in a waveform that ramps linearly from 0 A to 3 A in 2 seconds, stays at 3 A for 2 seconds, and then ramps linearly from 3 A down to 0 A in 1 second. What is the voltage across the inductor between t=4s and t=5s?

How are inductances combined when they are in series?

What is the primary purpose of using laminations for the cores of practical inductors?

In a pair of mutually coupled inductors, what is the purpose of the dot convention?

In the circuit model for a real capacitor shown in Figure 3.14, what does the parallel resistance Rp represent?

What is the equivalent inductance of a 3 H, 6 H, and 2 H inductor connected in parallel?

The charge on a 2 microfarad capacitor is given by q(t) = 10^-6 sin(10^5 t) C. What is the expression for the current, i(t)?

The voltage across a 150 microHenry inductance is a triangular waveform that ramps from 0 to 15 V in 2 microseconds, then ramps from 15 V to -15 V between 2 and 4 microseconds. What is the value of the current i(t) at t=2 microseconds, assuming i(0)=0?

What does the fluid-flow analogy for an inductor represent?

What is the equivalent capacitance of a 12 microfarad and a 24 microfarad capacitor connected in series?

What is the physical unit of inductance?

What must be true for the current i(t) in an inductor as long as the voltage v(t) across it is finite?

Two inductors, L1 = 1 H and L2 = 2 H, are mutually coupled with M = 1 H. The currents are i1(t) = sin(10t) and i2(t) = 0.5 sin(10t). Both currents are referenced into the dotted terminals. What is the voltage v1(t)?

In the circuit model for a real inductor, what does the parallel capacitance Cp, also known as interwinding capacitance, represent?

A voltage waveform v(t) shown in Figure 3.6(a) is applied to a 10 microfarad capacitor. The voltage ramps from 0 to 1000V in 1s, is constant at 1000V from 1s to 3s, and ramps from 1000V to 0 in 2s (from t=3s to t=5s). What is the current i(t) from t=0 to t=1s?

What is the equivalent inductance of a 4 H inductor in series with a parallel combination of a 3 H, 6 H, and 2 H inductor?

A 1 microfarad capacitor is being designed. If the dielectric is polyester (relative dielectric constant = 3.4) with a thickness of 15 micrometers, and the plates have a width of 2 cm, what is the required length L of the plates?

According to the text, what is a dielectric material?

Two capacitances of 2 microfarads and 1 microfarad are connected in series. What is their equivalent capacitance?

What is the primary trade-off mentioned in the text regarding the design of practical capacitors for compact electronic circuits?

In a pair of mutually coupled inductors where one current is referenced into a dotted terminal and the other is referenced out of a dotted terminal, what is the sign of the mutual inductance term in the voltage equations?

An initial charge q(0) is known for a capacitor C, and a current i(t) flows into it starting at t=0. Which equation correctly gives the voltage v(t) across the capacitor for t > 0?

What are ferrites, and why are they sometimes used for the cores of inductors?

In the context of the MATLAB Symbolic Toolbox described in Section 3.8, what is its primary function for analyzing circuits with inductors and capacitors?

What happens to the total stored energy in the circuit of Example 3.6 when the switch closes, connecting a 1 microfarad capacitor charged to 100V to an identical uncharged capacitor?

The current through a 10 mH inductor is i(t) = 0.1 cos(10^4 t) A. What is the expression for the stored energy, w(t)?

How do capacitances in parallel combine, and how does this compare to the rule for resistances?

An initial voltage v(0)=0 is across a 0.1 microfarad capacitor. The current is given by the square wave in Figure 3.7, which is +1 mA for 2 ms, then -1 mA for 2 ms, and so on. What is the voltage at t=2 ms?

Relative to mica, which has a relative dielectric constant of 7.0, how much larger is the capacitance of a parallel-plate capacitor if the dielectric is replaced with water, which has a relative dielectric constant of 78.5?

A 2 H inductor is connected to a 10 V DC source via a switch that closes at t=0. The initial current is zero. What is the current i(t) at t=1s?

What are the units of capacitance, and to what other units are they equivalent?

When combining inductors, what is the rule for a parallel combination, and how does it compare to the rule for resistors?

What is the stored energy w(t) in a 10 microfarad capacitor when the voltage across it, v(t), is given by the waveform in Figure 3.6(a), specifically at t=1s when the voltage is 1000V?

For the Linear Variable Differential Transformer (LVDT) described in Section 3.7, what is the output voltage vo(t) when the iron core is centered in the coils?

What is a 'parasitic element' in the context of a real capacitor or inductor?

A constant voltage of 12 V is applied to a 0.1 microfarad capacitor. What is the current flowing through the capacitor?

The voltage across a 0.1 microfarad capacitor is v(t) = 500[1 - cos(10^4 t)] V. What is the initial charge q(0) on the capacitor?

What is the alternative expression for stored energy in a capacitor, w(t), in terms of charge q(t) and capacitance C?

In the fluid-flow analogy, a capacitor is represented as a reservoir with an elastic membrane. What physical quantity in the capacitor is analogous to the displaced fluid volume starting from the unstretched membrane position?

A circuit contains two inductors in series, L1 and L2. How is their equivalent inductance, Leq, determined?