Example 19
150 kΩ
75 kΩ
1A
60 kΩ
15 kΩ
+
vab _
a
b
60 kΩ
15 kΩ
10 kΩ
50 kΩ
Use current division and voltage division to find the voltage vab across terminals a-b.
In this problem, we are trying to calculate the voltage across the terminals a and b.
Let’s consider the circuit, see if it is possible to simplify the circuit without affecting the
voltage vab. We first notice that the 150 kΩ resistor is in parallel with the 75 kΩ resistor
because the have the same pair of nodes. The equivalent resistance is
150  75 150

 50 k
150  75 2  1
So the two resistors is reduced to one resistor of 50 kΩ.
Similarly, the two 60 kΩ resistors are parallel connected since they have the same voltage
across them. To combine two identical resistances in parallel, we take the individual
resistance divided by 2, which gives us 30 kΩ.
For the simplified circuit, the current 1A is divided among the 3 parallel branches. The
current division says that the current through one of the resistors is proportional to the
total current. The constant proportionality is the ratio of the equivalent resistance of the 3
parallel resistors to the single resistance. For example, the equivalent resistance for this
problem is
1
240
240


 16 k
1
1
1
3  8  4 15
 
80 30 60
The current through the first branch should be the total current multiplied by the ratio of
the equivalent resistance to its resistance
1
16
 0 .2 A .
80
Through the second branch should be
1
16
 0.53 A
30
If we select the bottom node as the reference node. The voltage across the 30 kΩ resistor
v a  0.2  30 k  6kV
The voltage across the 15 k resistor is v a  0.53 15k  8kV .
The voltage across terminals a and b should be
v ab  v a  vb  6k  8k  2kV