Question

Which of the following combination of 7 identical capacitors each of $2\,\mu F$ gives a capacitance of $\frac{10}{11}\,\mu F$?

• A. 5 in parallel and 2 in series
• B. 4 in parallel and 3 in series
• C. 3 in parallel and 4 in series
• D. 2 in parallel and 5 in series

Hint:

Physics Tip: Remember that capacitors behave the opposite of resistors: series connection reduces total capacitance, while parallel connection increases it.

Answer 1

The Correct Option is A

Concept: Physics (Electrostatics) - Combinations of Capacitors.

Step 1: Recall the formulas for capacitor combinations.
• For $n$ identical capacitors connected in series, the equivalent capacitance is $C_{s} = \frac{C}{n}$.
• For $m$ identical capacitors connected in parallel, the equivalent capacitance is $C_{p} = mC$.

Step 2: Evaluate the specific combination for Option A. For 5 capacitors in parallel, $C_p = 5C = 5(2\mu F) = 10\mu F$. If this combination is then placed in series with 2 more capacitors, the net capacitance $C_{net}$ is found by: $$\frac{1}{C_{net}} = \frac{1}{C_p} + \frac{1}{C} + \frac{1}{C} = \frac{1}{10} + \frac{1}{2} + \frac{1}{2}$$ $$\frac{1}{C_{net}} = \frac{1}{10} + 1 = \frac{11}{10} \implies C_{net} = \frac{10}{11} \mu F$$ $$ \therefore \text{The correct combination is 5 in parallel and 2 in series.} $$