Page 35 - Schaum's Outline of Theory and Problems of Electric Circuits

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

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