Video Transcript
The circuit in the diagram contains
two capacitors connected in parallel. The total capacitance of the
circuit is 240 microfarads. What is the capacitance 𝐶?
In this question, we want to find
the capacitance 𝐶 of this capacitor that’s connected in parallel to this other
capacitor, whose value we’ve been given. To do this, we can recall that the
total capacitance for a parallel combination of capacitors is given by the sum of
the individual capacitances, 𝐶 one plus 𝐶 two and so on.
We only have two capacitors
connected in parallel in this circuit. So this equation simplifies to 𝐶
total equals 𝐶 one plus 𝐶 two. Let’s label the capacitor with
unknown capacitance 𝐶 as 𝐶 one and the other one as 𝐶 two. Since we want to find 𝐶 one, let’s
rearrange this equation to make 𝐶 one the subject. To do this, we simply subtract 𝐶
two from both sides of the equation, leaving us with 𝐶 one equals 𝐶 total minus 𝐶
two.
We know that the total capacitance
of the circuit 𝐶 total equals 240 microfarads, that 𝐶 two has a capacitance of 135
microfarads, and that 𝐶 one has a placeholder capacitance of 𝐶. If we substitute these values into
the equation, we get 𝐶 equals 240 microfarads minus 135 microfarads, which equals
105 microfarads. We have found that the capacitance
𝐶 is equal to 105 microfarads. So this is the final answer to this
question.
