Video Transcript
Two capacitors, 𝐶 one and 𝐶 two,
are connected in parallel, where 𝐶 one is greater than 𝐶 two. Which of the following statements
correctly relates the total capacitance, 𝐶 total, to 𝐶 one and 𝐶 two? (A) 𝐶 two is less than 𝐶 total,
which is less than 𝐶 one. (B) 𝐶 total equals the square of
𝐶 one plus 𝐶 two. (C) 𝐶 total equals 𝐶 one times 𝐶
two. (D) 𝐶 one equals 𝐶 total minus 𝐶
two. (E) 𝐶 total equals 𝐶 one over 𝐶
two plus 𝐶 two over 𝐶 one.
This question is asking us about
two capacitors connected in parallel. So, we could imagine a circuit like
this, where we have the two capacitors, 𝐶 one and 𝐶 two, on separate parallel
branches. We’re being asked how the total
capacitance, 𝐶 total, relates to these individual capacitances, 𝐶 one and 𝐶
two. To work this out, it will be
helpful to remember that the total capacitance for a parallel combination of
capacitors is given by 𝐶 total equals 𝐶 one plus 𝐶 two plus 𝐶 three and so
on. That is, for capacitors connected
in parallel, we add together the individual capacitances to find the total
capacitance of the combination.
In this case, we have just two
capacitors with capacitances 𝐶 one and 𝐶 two. So, this relationship would become
𝐶 total equals 𝐶 one plus 𝐶 two. Now, since 𝐶 total is equal to the
sum of 𝐶 one and 𝐶 two, we can discount answer option (A), which claims that 𝐶
total is larger than 𝐶 two but smaller than 𝐶 one. If 𝐶 total is the sum of the two
individual capacitances, then it must be larger than both 𝐶 one and 𝐶 two. Obviously, then, option (A) cannot
be correct.
To determine which of the four
remaining options is correct, let’s rearrange this equation by subtracting 𝐶 two
from each side. This gives us an equation that says
𝐶 one equals 𝐶 total minus 𝐶 two. Looking at the remaining answer
options we are given, we can see that our equation matches the one given in option
(D). We have found then that the correct
answer is given in option (D). The statement that correctly
relates the total capacitance 𝐶 total to the individual capacitances 𝐶 one and 𝐶
two is 𝐶 one is equal to 𝐶 total minus 𝐶 two.
