Kirchhoff's Laws

In the above discussion of energy we made two assumptions about electric circuits:

• The current entering one end of a wire connecting two devices is equal to the current leaving the other end. Thus, the current out of the generator in the left panel of figure 17.7 is assumed to equal the current into the capacitor.
• The net work done on a charged particle passing completely around a circuit loop is zero. Thus, the positive work done on charge passing through the generator in the right panel of figure 17.7 is exactly balanced by the potential difference across the inductor.

These are called Kirchhoff's laws. They are used extensively in electronic circuit design.

It is important to realize that Kirchhoff's laws are only approximations which hold when the currents and potentials in a circuit change slowly with time. For steady currents and constant potentials they are precisely true, since imbalances in charge entering and leaving a junction between devices would result in the indefinite buildup of charge in the junction with time and therefore an increasing electrostatic potential, which would violate the steady state assumption. Furthermore, a non-zero EMF around a closed loop would result in net acceleration of charge around the loop and a constantly increasing current.

If currents and potentials are changing with time, Kirchhoff's laws are approximately valid only if the capacitance, inductance, and resistance of the wires connecting circuit elements are much smaller than the capacitance, inductance, and resistance of the circuit elements themselves. For very high frequency operation, the effects of these ``parasitic'' properties are not small and must be included in the design of the circuit.