For the following circuit, determine the resistance viewed from

There are five problems in total. State how you derived your answer.
Problem 1 (18 points)
For the following circuit, determine the resistance viewed from
(1a) nodes A and D;
(1b) nodes A and C;
(1c) nodes B and D.
1 K⌦
2 K⌦
1 K⌦
4 K⌦
A D
B C
This exercise tells us that for the same circuit, viewing from different pair of
nodes we may get different resistance.
Problem 2 (22 points)
For the following circuit, show that the resistance seen from terminals A and
B will always be smaller than the smallest resistance among R1 and R2.
R1
A R2 B
1
Problem 3 (20 points)
Use the voltage divider pattern to make sense that vx = 5 V in the following
circuit. State your reasoning.
+ !
5 V
3 K⌦
+ vx !
Problem 4 (20 points)
Use the current divider pattern to determine ix.
24 mA
5 K⌦
4 K⌦

8 K⌦
Problem 5 (20 points)
Use some good combination of the basic analysis method, resistance equivalence, and/or circuit patterns to determine vx.
+ !
12 V
1 K⌦
4 K⌦
1 K⌦
2 K⌦
2 K⌦
+