Page 313 - Schaum's Outline of Theory and Problems of Applied Physics

298 DIRECT-CURRENTCIRCUITS [CHAP. 25

V e 10 V
(b) I 2 = = = 10 A
R 2 + r 0.5 + 0.5
2
2
P 2 = I R 2 = (10 A) (0.5 ) = 50 W
2
V e 10 V
(c) I 3 = = = 6.7A
R 3 + r 1 + 0.5
2
2
P 3 = I R 3 = (6.7A) (1 ) = 44 W
3

KIRCHHOFF’S RULES
The current that flows in each branch of a complex circuit can be found by applying Kirchhoff’s rules to the
circuit. The first rule applies to junctions of three or more wires (Fig. 25-9) and is a consequence of conservation
of charge. The second rule applies to loops, which are closed conducting paths in the circuit, and is a consequence
of conservation of energy. The rules are as follows:
1. The sum of the currents that flow into a junction is equal to the sum of the currents that flow out of the
junction.
2. The sum of the emf’s around a loop is equal to the sum of the IR potential drops around the loop.

Fig. 25-9

The procedure for applying Kirchhoff’s rules is as follows:

1. Choose a direction for the current in each branch of the circuit, as in Fig. 25-9. (A branch is a section of
a circuit between two junctions.) If the choice is correct, the current will turn out to be positive. If not,
the current will turn out to be negative, which means that the actual current is in the opposite direction.
The current is the same in all the resistors and emf sources in a given branch. Of course, the currents
will usually be different in the different branches.
2. Apply the first rule to the currents at the various junctions. This gives as many equations as the number
of junctions. However, one of these equations is always a combination of the others and so gives no
new information. (If there are only two junction equations, they will be the same.) Thus the number of
usable junction equations is equal to one less than the number of junctions.
3. Apply the second rule to the emf’s and IR drops in the loops. In going around a loop (which can be
done either clockwise or counterclockwise) an emf is considered positive if the − terminal of its source
is met first. If the + terminal is met first, the emf is considered negative. An IR drop is considered
positive if the current in the resistor R is in the same direction as the path being followed. If the current
direction is opposite to the path, the IR drop is considered negative.