Kirchafs Law

1. Kirchhoff’s Laws

Introduction

The circuits in this problem set are comprised of unspecified circuit elements. (We don’t know if a particular circuit element is a resistor or a voltage source or something else.) The current and voltage of each circuit element is labeled, sometimes as a value and sometimes as a variable. Some of these problems ask that we determine the value of a particular voltage or current. Other problems ask for the values of the power supplied or received by a particular circuit element. Kirchhoff’s laws are used to determine values of currents or voltages. The passive convention is used to decide if the product of a particular element current and voltage is the power supplied or received by the circuit element. The passive convention is discussed in Section 1.5 of Introduction to Electric Circuits (7e) by R. C. Dorf and J. A. Svoboda and summarized in Table 1.5-1. Kirchhoff’s laws are discussed in Section 3.2 of Introduction to Electric Circuits.

Worked Examples

Example 1: Consider the circuit shown in Figure 1. Determine the power supplied by element D and the power received by element F.

Figure 1. The circuit considered in Example 1 Solution: Figure 1 provides a value for the current in element D but not for the voltage, v, across element D. The voltage and current of element D given in Figure 1 do not adhere to the passive convention so the product of this voltage and current is the power supplied by element D. Similarly, Figure 1 provides a value for the voltage across element F but not for the current, i, in element F. The voltage and current of element F given in Figure 1 do adhere to the passive convention so the product of this voltage and current is the power received by element F.

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We need to determine the voltage, v, across element D and the current, i, in element F. We will use Kirchhoff’s laws to determine values of v and i. First, we identify and label the nodes of the circuit as shown in Figure 2.

Figure 2....