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Circuit Variables
Assessment Problems
AP To solve this problem we use a product of ratios to change units from
dollars/year to dollars/millisecond. We begin by expressing $10 billion in
scientific notation:
$100 billion = $100 x 109
Now we determine the number of milliseconds in one year, again using a
product of ratios:
1 year 1 day 1 hour 1 min 1 sec 1 year
.. . . .
days 24 hours 60 mins 60 secs 1000 ms X 109 ms
Now we can convert from dollars/year to dollars/millisecond, again with a
product of ratios:
$100 X 109 1 year 100
1 year x 109 IDS - = $
AP First, we recognize that 1 ns = 10-9 s. The question then asks how far a
signal will travel in 10-9 s if it is traveling at 80% of the speed of light.
Remember that the speed of light c = 3 X 108 m/ s. Therefore, 80% of c is
()(3 X 108) = X 108 m/s. Now, we use a product of ratios to convert
from meters/second to inches/nanosecond:
X 108 m 1 S 100 cm 1 in 8
---- ( x 10 )(100) ---- in
1s 109 ns 1m cm (109 )() 1 ns
Thus, a signal traveling at 80% of the speed of light will travel " in a
nanosecond.
1-1
1-2 CHAPTER 1. Circuit Variables
AP Remember from Eq. (), current is the time rate of change of charge, or
i = 11f In this problem, we are given the current and asked to find the total
charge. To do this, we must integrate Eq. () to find an expression for
charge in terms of current:
q(t) = lot i(x) dx
We are given the expression for current, i, which can be substituted into the
above expression. To find the total charge, we let t ----* 00 in the integral. Thus
we have
00
q = 1 20e-5000x dx = 20 e-50OOX!00 = 20 (e-OO _ eO)
total 0 -5000 0 -5000
20 20
- -5000(0 -1) = 5000 = C = 40ool1'C
AP Recall from Eq. () that current is the time rate of change of charge, or
i = 11f. In this problem we are given an expr