ABSTRACT
The laws which determine the currents and voltage drops in d.c. networks are: (a) Ohm’s law (see Chapter 2), (b) the laws for resistors in series and in parallel (see Chapter 5), and (c) Kirchhoff’s laws (see Section 13.2 following). In addition, there are a number of circuit theorems which have been developed for solving problems in electrical networks. These include:
(i) the superposition theorem (see Section 13.3), (ii) Thévenin’s theorem (see Section 13.5), (iii) Norton’s theorem (see Section 13.7), and (iv) the maximum power transfer theorem (see
Section 13.8)
Kirchhoff’s laws state:
(a) Current Law.At any junction in an electric circuit the total current flowing towards that junction is equal to the total current flowing away from the
Thus, referring to Fig. 13.1:
I1 + I2 = I3 + I4 + I5 or I1 + I2 − I3 − I4 − I5 = 0
(b) Voltage Law. In any closed loop in a network, the algebraic sum of the voltage drops (i.e. products of current and resistance) taken around the loop is equal to the resultant e.m.f. acting in that loop. Thus, referring to Fig. 13.2:
E1 − E2 = IR1 + IR2 + IR3 (Note that if current fl ws away from the positive terminal of a source, that source is considered by convention to be positive. Thus moving anticlockwise around the loop of Fig. 13.2, E1 is positive
Problem 1. (a) Find the unknown currents marked in Fig. 13.3(a). (b) Determine the value of e.m.f. E in Fig. 13.3(b).
