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1.5 Exercises

Exercise 1-1

The complement to voltage developed across an inductor due to the flow of electric current is the voltage developed across a capacitor, given as:

017equ01.jpg

Describe a mechanical (fluid-based) analogy for this electrical phenomenon.

Exercise 1-2

What is the electrical equivalent to Newton’s second law of motion,

017equ02.jpg

in the force-current analogy?

Exercise 1-3

An ideal capacitor of value 2 farads is charged to a voltage of 1V. An ideal inductor of value 2 henry is then instantaneously shorted across the capacitor terminals to form an LC tank circuit.

  1. Describe variations in voltage and current in the circuit formed.
  2. Calculate the peak current value that will flow through this ideal circuit.

It was stated in Section 1.4.1 that resonance leads to supply voltage “ringing,” or periodic variation in the power supply differential voltage. Why does supply voltage drop below the nominal value despite the fact that no power is consumed in the reactive components that cause this ringing?

Exercise 1-4

At nanoscale levels, current in a conductor is the flow of electrons propelled by an electric field that is created by the potential difference across the ends of the conductor. Each electron experiences a force corresponding to its charge, q, and the applied electric field in the conductor material.

What can be a principal phenomenon within the conductor structure at nanoscale levels that limits flow of electric current? What is the physical by-product of this phenomenon in the conductor? Why is this by-product quadratically related to the number of electrons passing through in a unit duration of time?

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