Video Transcript
The diagram shows an electric
circuit containing a cell and a bulb. The amount of charge flowing past
point 𝑃 in one second is 12 coulombs. If the amount of charge flowing
past point 𝑃 in one second were to double, by what factor would the current in the
circuit change?
Okay, since we’re talking about
current here, let’s begin by recalling what it is and how it’s measured. Electric current is the flow of
electric charge. And in a circuit, current measures
how much charge flows past a point in the circuit in one second. Now, in this circuit, we’ve been
told that a charge of 12 coulombs flows past point 𝑃 every second. But what we want to focus on is
this. If we were to double the amount of
charge that passes by point 𝑃 in one second, how would the current in the circuit
be affected? Specifically, by what factor would
the value of current change?
Keep in mind that when we say
factor here, we simply mean a number that multiplies some other number. For example, if we double the
charge passing point 𝑃, then we’re multiplying the charge passing point 𝑃 by a
factor of two. However, without even doing any
math, we might notice that the answer to this question can be found in the very
definition of electric current. Current is how much charge flows
past a point in one second. So, if we double how much charge
flows past a point in one second, which is the same thing as current, it makes sense
that we’re doubling the current itself. This is good evidence that the
answer is two.
Still, to be extra confident in our
answer, we can think about the mathematical relationship between charge and
current. Let’s recall the formula for
electric current: 𝐼 equals 𝑄 divided by 𝑡, where 𝐼 is the current, 𝑄 represents
charge, and 𝑡 is time. In this question, we’re thinking
about multiplying the charge 𝑄 by two and wondering how this would affect current
𝐼. Notice though that the value for
time 𝑡 is staying the same; it’s not changing. In both cases, with and without the
double charge, we’re only measuring how much charge flows past point 𝑃 in one
second. So we have a fraction.
If we double the numerator and just
leave the denominator as it is, how is the total value of the fraction affected? It doubles. Thus, if we double the amount of
charge passing through the circuit per second, we double the amount of current in
the circuit. All we must do now is remember that
to double the current means to multiply it by a factor of two.
So, just using our understanding of
electric current, we’ve determined that in the circuit if the amount of charge
flowing past point 𝑃 in one second were to double, the current in the circuit would
change by a factor of two.
