Page 197 - The Mechatronics Handbook

FIGURE 11.2 Illustration of Kirchhoff’s current law.

FIGURE 11.3 Voltages around a circuit.

points is called voltage. Thus, the units of voltage are those of energy per unit charge:
1 joule
1 volt = --------------------- (11.5)
coulomb
The voltage, or potential difference, between two points in a circuit indicates the energy required to
move charge from one point to the other. As will be presently shown, the direction, or polarity, of the
voltage is closely tied to whether energy is being dissipated or generated in the process. The seemingly
abstract concept of work being done in moving charges can be directly applied to the analysis of electrical
circuits; consider again the simple circuit consisting of a battery and a light bulb. The circuit is drawn
again for convenience in Fig. 11.3, and nodes are defined by the letters a and b. A series of carefully
conducted experimental observations regarding the nature of voltages in an electric circuit led Kirchhoff
to the formulation of the second of his laws, Kirchhoff’s voltage law, or KVL. The principle underlying
KVL is that no energy is lost or created in an electric circuit; in circuit terms, the sum of all voltages
associated with sources must equal the sum of the load voltages, so that the net voltage around a closed
circuit is zero. If this were not the case, we would need to find a physical explanation for the excess (or
missing) energy not accounted for in the voltages around a circuit. KVL may be stated in a form similar
to that used for KCL:
N
∑ v n = 0 Kirchhoff’s voltage law (11.6)

n=1
where the v n are the individual voltages around the closed circuit. Making reference to Fig. 11.3, we can
see that it must follow from KVL that the work generated by the battery is equal to the energy dissipated
in the light bulb to sustain the current flow and to convert the electric energy to heat and light:
v ab = – v ba

or
v 1 = v 2

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