Question

you need a capacitance of 25.0 μf, but you don't happen to have a 25.0 μf capacitor. you do have a 75.0 μf capacitor. what additional capacitor do you need to produce a total capacitance of 25.0 μf ?

Answer 1

To reach a total capacitance of 25.0 µF with a 75.0 µF capacitor, an implausible negative-value capacitor would theoretically be required. Hence, you cannot achieve 25.0 µF with a 75.0 µF capacitor and would need a different set of capacitors.

Step-by-step explanation:

To achieve a total capacitance of 25.0 µF using a 75.0 µF capacitor, you would need to connect an additional capacitor in series. The combined capacitance (Ctotal) of capacitors in series can be found using the formula 1/Ctotal = 1/C1 + 1/C2. Plugging in the known values, 1/25.0 µF = 1/75.0 µF + 1/C2, we can solve for C2, the value of the required additional capacitor.

First, we calculate the reciprocals: 1/25.0 µF = 0.04 µ
`f^(-1)`d 1/75.0 µF = 0.01333 µ
`f^(-1)` subtracting the reciprocal of the 75.0 µF capacitor from the total desired reciprocal gives us 0.04 µ
`f^(-1)` - 0.01333 µ
`f^(-1)`= 0.02667 µ
`f^(-1)`. To find the value of the required capacitor, C2, we take the reciprocal of this result, giving us approximately C2 = 1/0.02667 µ
`f^(-1)` ≈ 37.5 µF.

However, since we started with a capacitor that was larger than needed, the additional capacitor required has a negative capacitance, which is not possible in practice. This means that you cannot achieve a total capacitance of 25.0 µF using a 75.0 µF capacitor alone; instead, you would need a different combination of capacitors.