3.2 Ideal and real-world circuit elements

Source and linear circuit elements are ideal circuit elements. One central notion of circuit theory is combining the ideal elements to describehow physical elements operate in the real world. For example, the 1kresistor you can hold in your hand is not exactly an ideal 1kresistor. First of all, physical devices are manufactured to close tolerances (the tighter thetolerance, the more money you pay), but never have exactly their advertised values. The fourth band on resistors specifies theirtolerance; 10% is common. More pertinent to the current discussion is another deviation from the ideal: If a sinusoidalvoltage is placed across a physical resistor, the current will not be exactly proportional to it as frequency becomes high, sayabove 1MHz. At very high frequencies, the way the resistor is constructed introduces inductance and capacitanceeffects. Thus, the smart engineer must be aware of the frequency ranges over which his ideal models match reality well.

On the other hand, physical circuit elements can be readily found that well approximate the ideal, but they will alwaysdeviate from the ideal in some way. For example, a flashlight battery, like a C-cell, roughly corresponds to a 1.5V voltage source. However, it ceases to be modeled by a voltagesource capable of supplying any current (that's what ideal ones can do!) when the resistance of thelight bulb is too small.