1. How much work must be done to move 8.0 x 1020 electrons from one terminal on a 12-volt battery
to the other terminal?
First, we must know how much total charge is transferred.
q = # of electrons x charge on one electron
q = 8.0 x 1020 electrons ( -1.6 x 10-19 C per electron)
q = -130 C
Now work can be found as the product of the absolute value of this charge times the battery voltage.
W = q V = 130 C (12 volts) = 1500 J
2. If the transfer of charge described in problem 1 takes place in 7.0 seconds,
how much current is flowing when the battery is charging?
Here we use the basic definition of current:
I = q / t = 130 C / 7.0 s = 19 amperes
3. Now if the same battery is used to play a radio that draws a current of 0.016 amperes:
a. What is the internal resistance of the radio?
b. How long can we expect the radio to play on the charge given to the battery in
question #1 above?
a.
To find the resistance, we must use Ohm's law.
V = I Rso
R = V / I
Here V is still equal to 12 volts and the current (I) is 0.016 amperes:
R = 12 V / 0.016 A = 750 ohms
b.
The total charge on the battery is 130 C, which we are now transferring at a rate of
0.016 C per second. (Remember that one ampere = one coulomb per second.)
t = q / I = 130 C / 0.016 C per second = 8100 s (or about 2 1/4 h)
Batteries deliver dc current for use in our cars and for other portable
applications, but how about power consumption in our homes? Most people
think of 120 volts ac when they consider household use, but some of our
appliances require 240 volts ac, and large industrial machinery may need
440 volts ac or even higher. In our homes, only heavy power users such
as whole-house air conditioners and clothes dryers run on 240 volts ac,
so we will consider the 120 volt variety in the next few exercises. The
textbook provides several interesting problems dealing with these concepts.
For example, exercises 15 and 16 at the end of Chapter 8 deal with the
use of 120 volts ac in the home.
4. If an electrical appliance with a resistance of 40 ohms is connected to a 120 volt ac source,
how much current will flow through the appliance?
I = V / R = 120 V / 40 ohms = 3.0 A
5. How many 75-watt light bulbs could you plug into a 120 volt ac circuit
without blowing a 15-ampere fuse?
First, let's see how much power one 75-watt bulb uses. As a matter of fact,
75 watts is the power used, so what we really need to know is how many amps
each bulb draws or how much power the 15-amp circuit can supply. Let's do
the calculation using current draw.
I = P / V = 75 W / 120 V = 0.63 A per bulb
A 15-ampere circuit can light:
# of bulbs = 15 A / 0.63 A per bulb = 23.8 bulbs
Because we can't have part of a bulb burning, the 15-ampere circuit
will work for 23 bulbs, but if we try to plug in the 24th one, the
fuse will blow. This protection keeps the wiring in our homes from
overheating and causing fires or other damage.
6. How much current does a 1600-watt hair dryer draw and
how much resistance does it have?
Again we will assume the hair dryer is plugged into a 120 V ac.
I = P / V = 1600 W / 120 V = 13.3 A
R = V / I = 120 V / 13.3 A = 9.02 ohms
R = 9.0 ohms (to 2 significant figures)
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