In the application of Kirchoff’s
Laws to electrical networks, there has always been questions on the proper
direction of current to assume. The direction of current assumed should not be
a thing to be worried about. The direction of flow of current can be assumed to
be either clockwise or anti-clockwise. If the assumed direction of current is
not the actual direction, then on solving the question, the current will be
found to have a minus sign. If the answer is positive, then the assumed current
is the same as the actual direction. However, the important point is that once
a particular direction has been assumed, the same should be used throughout the
solution of the question.
Note: It should be noted that Kirchoff’s Laws are applicable both
to d.c. and a.c. voltages and currents. However, in the case of alternating
currents, any e.m.f. of self-inductance or that existing across a capacitor
should also be taken into account.
to d.c. and a.c. voltages and currents. However, in the case of alternating
currents, any e.m.f. of self-inductance or that existing across a capacitor
should also be taken into account.
Example
Calculate the current in the 7Ω
resistor in the figure shown below. All values of resistors are in Ohms.
resistor in the figure shown below. All values of resistors are in Ohms.
Solution
Applying KVL to each loop, we
have;
have;
At loop 1,
(5+4+7)I1 – 7I2
– 4I3 = -5
– 4I3 = -5
16I1 – 7I2
– 4I3 = -5 – – – – – – – – – – – — – – – (1)
– 4I3 = -5 – – – – – – – – – – – — – – – (1)
At loop 2,
(7+2+1)I2 – 7I1
– I3 = 0
– I3 = 0
-7I1 + 10I2
– I3 = 0 – – – – – – – – – – – – – – – – (2)
– I3 = 0 – – – – – – – – – – – – – – – – (2)
At loop 3,
(4+3+1) I3 – 4I1
– I2 = 5
– I2 = 5
-4I1 – I2 +
8I3 = 5 – – – – – – – – – – – – – – — – (3)
8I3 = 5 – – – – – – – – – – – – – – — – (3)
Equation (1), (2) and (3) can be
solved simultaneously using matrix method.
solved simultaneously using matrix method.
Note: The negative sign in the
value of the current flowing through I7 means that the actual
direction of current is in opposition to that assumed in analysing the mesh.
value of the current flowing through I7 means that the actual
direction of current is in opposition to that assumed in analysing the mesh.
