## PHYS345 Electricity and Electronics

**Hints for 9/7 Assignment**

**Hint for S3.1a**
The nodal equation is

- 2 + *V*_{1}/4 + (*V*_{1} + 10)/2 = 0.

**Hint for S3.2a**

The nodal equation is

- 6 + (*V*_{1} - 18)/3 + *V*_{1}/6 - 3 = 0.

**Hint for 3.4**

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 V_{1}, V_{2}, and V_{3} from left to right.
The nodal equation for the node on the far left is then:

2 + (V_{1} - V_{2}) + (V_{1} - V_{3})^{.}2 = 0.

Write down the remaining two nodal equations and solve for V_{2}.

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

**Hint for 3.5**

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:
V_{1}, V_{2}, V_{3}, and the unknown current.
However, please notice that V_{3} - V_{2} = 3 V,
which quickly provides the needed fourth equation.

The nodal equation for the middle node may be written as:

(V_{2} - V_{1})^{.}2 + V_{2}^{.}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.