40 CIRCUIT CONCEPTS
all currents (entering or leaving) at any node is zero, or no node can accumulate or store charge.
Figure 1.3.1 illustrates Kirchhoff’s current law, in which at nodea,i 1 −i 2 +i 3 +i 4 −i 5 =0or−i 1 +i 2 −i 3 −i 4 +i 5 = 0
or i 1 +i 3 +i 4 =i 2 +i 5 (1.3.1)Note that so long as one is consistent, it does not matter whether the currents directed toward the
node are considered positive or negative.
KVL states that thealgebraicsum of the voltages (drops or rises) encountered in traversing
anyloop(which is aclosed paththrough a circuit in which no electric element or node is
encountered more than once) of a circuit in a specified direction must be zero. In other words, the
sum of the voltage rises is equal to the sum of the voltage drops in a loop. A loop that contains no
other loops is known as amesh. KVL implies that moving charge around a path and returning to the
starting point should require no net expenditure of energy. Figure 1.3.2 illustrates the Kirchhoff’s
voltage law.
For the mesh shown in Figure 1.3.2, which depicts a portion of a network, starting at nodeaand
returning back to it while traversing the closed pathabcdeain either clockwise or anticlockwise
direction, Kirchhoff’s voltage law yields−v 1 +v 2 −v 3 −v 4 +v 5 =0orv 1 −v 2 +v 3 +v 4 −v 5 = 0
or v 1 +v 3 +v 4 =v 2 +v 5 (1.3.2)Note that so long as one is consistent, it does not matter whether the voltage drops are considered
positive or negative. Also notice that the currents labeled in Figure 1.3.2 satisfy KCL at each of
the nodes.i (^4) i 5
i 2
i 1
i 3
Node a
Figure 1.3.1Illustration of Kirchoff’s current law.
Box 5
Box 3
Box 2
c
d
e
a
b
Dependent source
−
−
−
−
−
i 2 i 3
v 2
v 1
Av 2 = v 4
v 5
v 3
i 1
i 5
i 1 − i 5
i 1 − i 2
i 2 + i 3
i 3 + i 4
i 4 − i 5
i 4
Figure 1.3.2Illustration of Kirchhoff’s
voltage law.