If a standard type of LED light
bulb operates at a 20-milliampere electric current, what time will it take 6.5 times
10 to the 17 electrons to flow past a point in the bulb filament? Use the charge of an electron 1.60
times 10 to the negative 19 coulombs.
Here, we are told that a standard
LED light bulb operates at a 20-milliampere electric current. We are asked how much time it would
take for 6.5 times 10 to the 17 electrons to flow past a point in the filament of
the bulb, given that the charge of the electron is 1.60 times 10 to the negative 19
coulombs. Let’s recall that current 𝐼 is
equal to the amount of charge 𝑄 moving past a point divided by the time 𝑡 that it
takes that charge to move.
Because we are trying to find the
time it takes for electrons to flow past a point, we need to rearrange this equation
to make 𝑡 the subject. We can do this by multiplying both
sides of the equation by 𝑡 over 𝐼. We can then cancel the 𝑡’s on the
right-hand side and the 𝐼’s on the left-hand side. This leaves us with an equation
that says the time 𝑡 that it takes for an amount of charge to move past a point is
equal to 𝑄, the total amount of charge moving past the point, divided by the
So, we have the equation we need to
solve this problem. However, we still don’t have a
value for the total charge that is flowing through the point. What we do know is though we are
interested in the amount of time it takes for 6.5 times 10 to the 17 electrons to
pass the point, we need to figure out how much charge this is equal to. The total charge will be equal to
the number of electrons multiplied by the charge of each individual electron. We’re told that the charge of one
electron is 1.60 times 10 to the negative 19 coulombs.
So, we have that the total charge,
which is our value of 𝑄, is equal to 6.5 times 10 to the 17 multiplied by 1.60
times 10 to the negative 19 coulombs. This is equal to 0.104 coulombs of
charge. Now that we have a value for the
total charge moving through the point as well as the current 𝐼 through the point,
we can solve this equation that we found earlier for the time. We have that the time 𝑡 that it
takes for 6.5 times 10 to the 17 electrons to travel through a point in the bulb
filament is equal to 0.104 coulombs divided by 20 milliamperes. Before we evaluate this, we’ll need
to convert the units of milliamperes into units of amperes.
One ampere is equal to 1000
milliamperes. To convert from milliamperes to
amperes then, we need to divide by a factor of 1000. That means that 20 milliamperes is
equal to 0.02 amperes. Now, on the right-hand side of our
equation, we have a charge in coulombs divided by a current in amperes. Let’s recall, though, that units of
amperes are equivalent to units of coulombs per second.
Replacing the amperes by coulombs
per second, we can see that the units of coulombs then cancel from the numerator and
denominator. We’re left with units of one
divided by one over seconds, which is simply units of seconds. Then, evaluating the expression, we
have that 0.104 divided by 0.02 is equal to 5.2. And so, we have found that the time
𝑡 is equal to 5.2 seconds.
Our final answer then is that it
takes 5.2 seconds for 6.5 times 10 to the 17 electrons to flow past a point in this