Video Transcript
If an electric device that works at
a 0.05-ampere electric current draws 4.25 coulombs of charge, then the time taken by
the charge to flow is blank seconds. (A) 85, (B) 170, (C) 4.5, (D)
90.
In this problem, we are told that a
particular electric device works at an electric current of 0.05 amperes and draws
4.25 coulombs of charge during some interval of time. We are asked to figure out what
this time interval is, that is, how long it would take this device to draw the given
amount of charge at the given current. Let’s begin by reminding ourselves
of the equation that defines electric current.
The electric current through a
point is equal to the total charge that flows through that point in a given amount
of time divided by the length of time that it took for that charge to flow. We can write this using symbols as
current 𝐼 is equal to charge 𝑄 divided by time 𝑡. Because the question is asking us
to find the time it takes for the charge to flow, we need to rearrange this equation
to make time 𝑡 the subject.
We can do this by first multiplying
both sides by 𝑡. Canceling the 𝑡’s on the
right-hand side, we have that 𝑡 times 𝐼 is equal to 𝑄. Then, we can divide both sides by
𝐼. Canceling the 𝐼’s on the left, we
have that time 𝑡 is equal to charge 𝑄 divided by current 𝐼. We can now substitute in our values
for the charge drawn 𝑄 and the current 𝐼. We have that 𝑄 equals 4.25
coulombs, and 𝐼 equals 0.05 amperes. Substituting these values, we have
that 𝑡 is equal to 4.25 coulombs divided by 0.05 amperes.
Before evaluating this expression,
let’s take a look at the units that we have. On the right-hand side, we have
units of coulombs divided by units of amperes. Remember, though, that amperes are
equivalent to coulombs per second. If we replace the units of amperes
by coulombs per second in this expression, we can see that the coulombs then cancel
from the numerator and denominator on the right-hand side. We’re then left with units of one
over one over seconds, which is simply equal to units of seconds. This is good, because seconds are a
valid unit of time. And we can notice from the question
text that we’re expected to give our answer in these units of seconds.
Let’s now evaluate the
expression. The time that it takes for this
device to draw the charge is equal to 4.25 divided by 0.05, with units of
seconds. This works out as 85 seconds. This means that it takes 85 seconds
for this electric device to draw 4.25 coulombs of charge at an electric current of
0.05 amperes. This number of seconds is the value
given in option (A). That means that option (A), 85, is
the correct answer.
