Video Transcript
A television works at an electric
current of 0.5 amperes. If the television is turned on for
1.5 hours, then the electric charge that passes through it is blank coulombs. (A) 10800, (B) 5400, (C) 2700, (D)
450.
Here, we are told that a television
works at an electric current of 0.5 amperes. We are also told that the
television is turned on for 1.5 hours. And we are asked to figure out how
much electric charge passes through it during that time.
We can solve this problem using the
equation to define electric current. So let’s recall what that equation
is. The current through a point is
equal to the total charge that flows through the point divided by the time it takes
for that charge to flow. We can write this symbolically as
𝐼, the current, is equal to 𝑄, the charge, divided by 𝑡, the time. We have values for the current and
time, and we want to find the charge that flowed through the television in that
time. This means that we need to
rearrange the equation to make 𝑄 the subject. We can do this by multiplying both
sides by the time 𝑡. Canceling the 𝑡’s on the
right-hand side, we have that 𝑄 is equal to 𝐼 multiplied by 𝑡.
Before we substitute in our values
for the time and current, let’s consider the units of these quantities. The current 𝐼 is given in units of
amperes, which is the standard SI unit for current. However, the value we are given for
the time 𝑡 is in units of hours. We need to convert this into a
value in units of seconds before we can use it in the equation we found. There are 60 minutes in one
hour. So, to convert from hours to
minutes, we multiply by a factor of 60. Then, there are 60 seconds in one
minute. So, to convert from minutes to
seconds, we multiply by another factor of 60. Completing the calculation, we find
that the time of 1.5 hours is equal to 5400 seconds.
We can now substitute our values
for the current 𝐼 and the time 𝑡 into our equation for the charge 𝑄. We find that the total electric
charge that flows through the television is equal to 0.5 amperes multiplied by 5400
seconds. On the right-hand side, we can note
that the units of amperes are equivalent to units of coulombs per second. Replacing the amperes by coulombs
per second, we see that the units of seconds and per second then cancel each other
out. This leaves us with units of
coulombs. This is a good sign. We can recognize coulombs as a
valid unit of charge and the unit that is used in the question text.
Let’s now evaluate this
expression. We have that the total electric
charge 𝑄 is equal to 0.5 multiplied by 5400 in units of coulombs. Multiplying these values, we find
that 𝑄 is equal to 2700 coulombs. That is, we have worked out that
2700 coulombs of electric charge passed through the television. This matches the value given in
option (C). Therefore, the correct answer is
option (C), 2700.
