Question

Suppose you want a capacitor bank with a total capacitance of 0.750 F, and you have numerous 1.50 mF capacitors. What is the smallest number you could hook together to achieve your goal, and how would you connect them?

a) 500 capacitors connected in series
b) 500 capacitors connected in parallel
c) 250 capacitors connected in series
d) 250 capacitors connected in parallel

Answer 1

To achieve a total capacitance of 0.750 F with 1.50 mF capacitors, one would need to connect 500 capacitors in parallel configuration.

Step-by-step explanation:

When trying to achieve a desired total capacitance with multiple capacitors, you have the option to connect them in series or parallel.

In a parallel configuration, the total capacitance (Cp) is the sum of the individual capacitances. Conversely, in a series setup, the reciprocal of the total capacitance (1/Cs) is the sum of the reciprocals of the individual capacitances. Therefore, to get the largest total capacitance, capacitors must be connected in parallel.

For the scenario of wanting a capacitor bank with a total capacitance of 0.750 F using 1.50 mF capacitors, you would need to connect them in parallel. Since 1.50 mF (which is equal to 0.0015 F) multiplied by 500 gives us 0.750 F, you would need 500 capacitors connected in parallel to achieve the goal.