1250
F 14
EX:
HOMEWORK #2-2 prob 1 solution
N. Cotter
Determine which of the following statements follow from Kirchhoff's or Ohm's law.
a)
Any network consisting of only resistors between two terminals may be
replaced by a single equivalent resistor.
b)
The sum of currents flowing out of any bubble drawn around part of a circuit
must be zero.
c)
The sum of voltage drops around any loop must be zero, even if the loop crosses
open circuits or follows part of its own path twice or more.
SOL'N:
All of the statements are true. The equivalent resistance statement does
depend on Kirchhoff's laws for its proof, but the key ingredient is the
linearity of Ohm's law. That is, doubling the applied voltage will double
the current everywhere in the resistor network.
To prove the statement about currents flowing out of any bubble, observe
that, for neighboring nodes, the currents flowing out of neighboring nodes
toward each other are equal but opposite in sign. So they cancel out.
Kirchhoff's voltage law allows for voltage drops across open circuits, and
a path that crosses itself or traces part of its path more than once is
equivalent to several simple loops summed together. Each of the simple
loops has voltage drops that sum to zero, so the sum of those loops is zero.