**Examples
for Resistors**

Example #1

Problem:

A wire of length *L*
= 60 *m* needs to be laid to carry a current of 150 amps
with a voltage drop of no more than 0.5 *V*. The wire is
to be made of copper which has a resistivity r* = *1.72E-8 W*m*. What is the
minimum diameter *D *of the wire?

Solution:

The resistance of the wire needs to by less than the voltage drop divided by the current.

The resistance is
given by R = r*L/A*, therefore the cross sectional
area is:

D =
1.99 *cm*

Example #2

Problem:

Consider the
circuit below. What is the equivalent resistance *R*_{ab}?

DATA:
*R*_{1} = R_{2} = R_{3} =
7.0 W

Solution:

First consider the upper two
resistors as a single resistor, *R*_{23}*.
*The resistance *R*_{AB} can be found
by adding *R*_{1 }and *R*_{23
}in parallel.

Adding one 1/14 and 1/7 gives 3/14, therefore

*R*_{AB}
= (14/3) W

Example #3

Problem:

What is the
equivalent resistance *R*_{AB} of the
three resistors shown below.

Data *R*_{1}*
= R*_{2}* = R*_{3}*
=* 6 W.

Solution:

Use the relation
to solve for *R*_{AB}*.*

*R*_{AB}
= 2 W

Example #4

Problem:

A 12-volt battery
is used to heat a 120 *ml* cup of coffee by submerging an
8.0-ohm resistor. How long will take to bring the coffee from 20 ^{o}C
to 100 ^{o}C?

Solution:

The energy needed to heat the water is:

where *C*_{v}
is the specific heat, one calorie per gram, D*T* is
the change in temperature and *m* is the mass, 120 *g. *One
then obtains the energy, *E* = 9600 calories = 4.03E4 *J*.
The time D*t* can be found by

Dt = 37 minutes