Question

Four capacitors of equal capacity have an equivalent capacitance \(C_1\) when connected in series and an equivalent capacitance \(C_2\) when connected in parallel. The ratio \(\dfrac{C_2}{C_1}\) is

• A. \(4\)
• B. \(12\)
• C. \(16\)
• D. \(8\)

Hint:

For identical capacitors, parallel combination increases capacitance while series combination decreases it.

Answer 1

The Correct Option is C

Step 1: Assume capacitance of each capacitor.
Let each capacitor have capacitance \(C\).

Step 2: Equivalent capacitance in series.
For four capacitors in series, \[ \frac{1}{C_1} = \frac{1}{C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C} = \frac{4}{C} \Rightarrow C_1 = \frac{C}{4} \]

Step 3: Equivalent capacitance in parallel.
For four capacitors in parallel, \[ C_2 = C + C + C + C = 4C \]

Step 4: Find the ratio.
\[ \frac{C_2}{C_1} = \frac{4C}{C/4} = 16 \]