Circuit Laws 3.1

INTRODUCTION

An electric circuit or network consists of a number of interconnected single circuit elements of the type described in Chapter 2. The circuit will generally contain at least one voltage or current source. The arrangement of elements results in a new set of constraints between the currents and voltages. These new constraints and their corresponding equations, added to the current-voltage relationships of the individual elements, provide the solution of the network. The underlying purpose of deﬁning the individual elements, connecting them in a network, and solving the equations is to analyze the performance of such electrical devices as motors, generators, transformers, electrical transducers, and a host of electronic devices. The solution generally answers necessary questions about the operation of the device under conditions applied by a source of energy.

3.2

KIRCHHOFF’S VOLTAGE LAW

For any closed path in a network, Kirchhoﬀ’s voltage law (KVL) states that the algebraic sum of the voltages is zero. Some of the voltages will be sosurces, while others will result from current in passive elements creating a voltage, which is sometimes referred to as a voltage drop. The law applies equally well to circuits driven by constant sources, DC, time variable sources, vðtÞ and iðtÞ, and to circuits driven by sources which will be introduced in Chapter 9. The mesh current method of circuit analysis introduced in Section 4.2 is based on Kirchhoﬀ’s voltage law. EXAMPLE 3.1. Write the KVL equation for the circuit shown in Fig. 3-1.

Fig. 3-1