## PHYS345 Electricity and Electronics

Hints for 9/7 Assignment

Hint for S3.1a

The nodal equation is
- 2 + V1/4 + (V1 + 10)/2 = 0.

The nodal equation is
- 6 + (V1 - 18)/3 + V1/6 - 3 = 0.

First, remember that the conductance G plays the role of a reciprocal resistance. Thus a 4 S conductor has a resistance of 0.25 ohm. Also Ohm's law V=IR may be written as I=VG, a form which is well adapted to nodal analysis.

There are three non-trivial nodes; I choose labels V1, V2, and V3 from left to right. The nodal equation for the node on the far left is then:
2 + (V1 - V2) + (V1 - V3).2 = 0.

Write down the remaining two nodal equations and solve for V2.

You may find a Linear Algebra Solver to be useful in finding the final answer.

Here again, there are three non-trivial nodes; at first glance there would seem to be a problem -- three nodal equations and four unknown quantities: V1, V2, V3, and the unknown current. However, please notice that V3 - V2 = 3 V, which quickly provides the needed fourth equation.

The nodal equation for the middle node may be written as:
(V2 - V1).2 + V2.4 + I = 0.

"http://www.physics.udel.edu/~watson/phys345/protected/exercises/hints/0907.html"
Last updated Sept. 13, 1999.
Copyright George Watson, Univ. of Delaware, 1999.