PRACTICE EXAM 1 PROBLEM 1 SOLUTION
1250
F 14
EX:
Find the resistance, Req, seen looking into the terminals of the network below.
SOL'N:
Coloring the nodes helps to identify what is going on.
In the lower right, we discover that R5 is shorted out by a wire. This
means the voltage across R5 is zero. By Ohm's law, there is no current
flow in R5. Since no current flows in R5, removing it from the circuit
(leaving an open circuit) will make no difference.
Pushing parts in on the right side and redrawing makes it easier to
understand what is going on.
On top, we have R1 and R2 in series, since there is no branching in the
wire between them. Thus, we can combine R1 and R2.
From the colors of the nodes, we see that all three resistances are
connected to the same color (green) on one side and to the same color
(blue) on the other side. Thus, all three resistances are in parallel.
Redrawing, we have the following circuit.
We now compute the parallel resistance by using the conductance
formulation, which works for any number of resistors in parallel.
Req =
1
1
1
1
+
+
2.4 MΩ 1.2 MΩ 200 kΩ
Req =
1
2.4 MΩ 2.4 MΩ
⋅
=
= 160 kΩ
1
1
1
2.4
MΩ
1+
2
+
12
+
+
2.4 MΩ 1.2 MΩ 200 kΩ
or