### Video Transcript

Two capacitors, πΆ one and πΆ two,
are connected in parallel, where πΆ one is greater than πΆ two. Which of the following statements
correctly relates the total capacitance, πΆ total, to πΆ one and πΆ two? (A) πΆ two is less than πΆ total,
which is less than πΆ one. (B) πΆ total equals the square of
πΆ one plus πΆ two. (C) πΆ total equals πΆ one times πΆ
two. (D) πΆ one equals πΆ total minus πΆ
two. (E) πΆ total equals πΆ one over πΆ
two plus πΆ two over πΆ 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, πΆ one and πΆ two, on separate parallel
branches. Weβre being asked how the total
capacitance, πΆ total, relates to these individual capacitances, πΆ one and πΆ
two. To work this out, it will be
helpful to remember that the total capacitance for a parallel combination of
capacitors is given by πΆ total equals πΆ one plus πΆ two plus πΆ 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 πΆ one and πΆ two. So, this relationship would become
πΆ total equals πΆ one plus πΆ two. Now, since πΆ total is equal to the
sum of πΆ one and πΆ two, we can discount answer option (A), which claims that πΆ
total is larger than πΆ two but smaller than πΆ one. If πΆ total is the sum of the two
individual capacitances, then it must be larger than both πΆ one and πΆ two. Obviously, then, option (A) cannot
be correct.

To determine which of the four
remaining options is correct, letβs rearrange this equation by subtracting πΆ two
from each side. This gives us an equation that says
πΆ one equals πΆ total minus πΆ 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 πΆ total to the individual capacitances πΆ one and πΆ
two is πΆ one is equal to πΆ total minus πΆ two.