What is the total capacitance of three capacitors valued at 100pF, 100pF, and 50pF when connected in series?

When capacitors are connected in series, the total capacitance can be calculated using the formula:

1/C_total = 1/C1 + 1/C2 + 1/C3

In this case, the values of the capacitors are 100 pF, 100 pF, and 50 pF. Plugging these values into the formula gives:

1/C_total = 1/100 + 1/100 + 1/50

The fractions can be summed up:

• The first two capacitors, each at 100 pF, contribute 1/100 + 1/100, which simplifies to 2/100 or 1/50.
• The 50 pF capacitor contributes 1/50.

Combining these gives: 1/C_total = 1/50 + 1/50 = 2/50 = 1/25

To find the total capacitance, C_total, we take the reciprocal:

C_total = 25 pF

Thus, the total capacitance of the three capacitors in series is 25 pF. This method of calculating series capacitance captures the essential principle that in series configurations, the inverse of the total capacitance is the sum of the