Final answer:
The total capacitance of a 20 µF and a 30 µF capacitor connected in series is 12 µF. This is calculated by taking the reciprocal of the sum of the reciprocals of their individual capacitances. option a is correct.
Step-by-step explanation:
When two capacitors are connected in series, the total capacitance is affected differently than if they were in parallel. To calculate the total capacitance of capacitors in series, we use the formula:
1/Ctotal = 1/C1 + 1/C2
In this case, we have a 20 µF and a 30 µF capacitor connected in series. Plugging these values into our formula, we get:
1/Ctotal = 1/20 µF + 1/30 µF = 3/60 µF + 2/60 µF = 5/60 µF
Now, we take the reciprocal of this value to solve for Ctotal:
Ctotal = 60 µF / 5 = 12 µF
The total capacitance of the two capacitors connected in series is, therefore, 12 µF.