Video Transcript
If a filament of a light bulb
experiences a current of 0.3 amperes, the electric charge that will flow through a
point P in the filament in 25 seconds will be blank. (A) Five coulombs, (B) 12 coulombs,
(C) 8.3 coulombs, (D) 7.5 coulombs.
Here, we are asked to consider a
filament of a light bulb with a current of 0.3 amperes through it. We are asked to figure out how much
charge will flow through a point P in the filament during a time period of 25
seconds.
In order to answer this question,
it’ll help to recall that electric current is defined as the rate of flow of charge
over time. The equation defining the electric
current through a point is current 𝐼 is equal to the charge 𝑄 that flows through
that point divided by the time 𝑡 that it takes for that charge to flow. In this problem, we know that the
current 𝐼 is equal to 0.3 amperes and the time 𝑡 is 25 seconds.
We are trying to calculate an
amount of charge, which means we need to rearrange this equation to make charge 𝑄
the subject. We can do this by multiplying both
sides of the equation by 𝑡. Then, after canceling the 𝑡’s on
the right-hand side, we get an equation that says charge 𝑄 is equal to current 𝐼
multiplied by time 𝑡. We can now substitute in our values
for the current 𝐼 and the time 𝑡. We find that 𝑄 is equal to 0.3
amperes multiplied by 25 seconds.
Before we evaluate this expression,
let’s take a look at the units we have on the right-hand side. We have a current in units of
amperes and a time in units of seconds. We can remember though that units
of amperes are equivalent to units of coulombs per second. If we replace the units of amperes
by units of coulombs per second in this expression, we can see that the seconds and
per second cancel each other out. This leaves us with units of
coulombs. And we can recall that the coulomb
is the unit for electric charge, which means we know we have the right units
here.
Now that we know our units are
correct, we can solve this equation. The charge 𝑄 is equal to 0.3
multiplied by 25, with units of coulombs. This is equal to 7.5 coulombs. This matches the value given in
option (D). Therefore, the correct answer is
option (D), 7.5 coulombs.
