## PHYS345 Electricity and Electronics

**Quiz 3 Solution:** Thévenin Generator

Construct a Thévenin generator to determine the voltage across the 5 ohm resistor shown?

**1. Find ***R*_{TH} by killing the sources.

*R*_{TH} = 1 ohm + 2 ohm || 3 ohm.

*R*_{TH} = 2.2 ohm.

**2. Find ***V*_{oc} by circuit analysis.

Since we are looking for the open-circuit voltage, I would recommend nodal analysis.
If we solve for *V*_{1} we will be most of the way to the complete solution
since
*V*_{oc} = *V*_{1} + 2 V.
The 2 V comes from the voltage drop across the 1 ohm resistor that
has 2 A current through it from the current source.

KCL at node 1: (*V*_{1}-2)/2 + *V*_{1}/3 -2 = 0.

3(*V*_{1}-2) +2*V*_{1} - 12 = 0

5*V*_{1} = 18

*V*_{1} = 3.6 V

*V*_{oc} = 5.6 V
**3. Use Thévenin generator to complete circuit analysis.**

The voltage across the 5 ohm resistor is (5.6 V) (5.0 ohm) / 7.2 ohm) = 3.9 V.

*Thanks go to Eddie Knotts for reporting an error in way the current source
was killed in the original version of the figure in Part 1.*

"http://www.physics.udel.edu/~watson/phys345/quiz/03soln.html"

Last updated Oct. 31, 1999.

Copyright George Watson, Univ. of Delaware, 1999.