Cables allow us to transmit electrical signals from one circuit to another. For example, we might attach coaxial cable between a function generator and an oscilloscope (Figure 4.1a) and plastic-coated twin lead between an antenna and a television (Figure 4.1b). Usually, when we analyze the circuit, we assume that the voltage at one end of the cable is the same as the voltage at the other end and that the current at the beginning is the same as the current at the end. This is appropriate if the frequency is low. However, at high frequencies the cable itself begins to have an effect. A fundamental limitation is the speed of light. If the voltage at one end of the cable changes appreciably in less time than it takes light to propagate to the other end, we should expect the voltage to be different at the two ends. Another way of saying this is that we would expect the voltages at the ends to be different when the length of the cable becomes an appreciable fraction of a wavelength.

Distributed Capacitance and Inductance

However, even when the cable is considerably shorter than a wavelength, it can have a large effect. We found in Problem 3 that a cable has capacitance. This capacitance is associated with the charges that the voltages on the line induce. We can take the capacitance into account in a circuit by adding a capacitance between the wires (Figure 4.1c).