Page 121 - Basic Electrical Engineering

or, − I R − (I − I ) R − E = 0 (iii)
1
3
2
2
2
2
In the two equations, i.e., in (ii) and (iii), if the values of R , R , R , E , and
1
2
1
3
E , are known, we can calculate the branch currents by solving these
2
equations.
Students need to note that Kirchhoff’s laws are applicable to both dc and
ac circuits.
Let us apply KVL in a circuit consisting of a resistance, an inductance, and
a capacitance connected across a voltage source as has been shown in Fig.

2.21. We will equate the voltage rise with the voltage drops.

Figure 2.21 Application of KVL

The voltage equation is

While solving network problems using Kirchhoff’s laws we frame a
number of simultaneous equations. These equations are solved to determine

the currents in various branches in a circuit. We will discuss solving of
simultaneous equations by the method of determinants or Cramer’s Rule.

2.5.3 Solution of Simultaneous Equations Using Cramer’s Rule

Let the three simultaneous equations written for a network problem be of the
form

a x + b y + c z = d 1
1
1
1