Question

The equivalent capacitance of capacitors connected in series is

• A. \(C_1+C_2+C_3\)
• B. \(\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}\)
• C. \(\frac{1}{C_{\text{eq}}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}\)
• D. Greater than the largest capacitance

Hint:

For capacitors in series, use reciprocal addition.

Answer 1

The Correct Option is C

Concept: In series connection of capacitors, charge on each capacitor is same and voltage divides.

Step 1: For capacitors in series: \[ \frac{1}{C_{\text{eq}}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\cdots \]

Step 2: The equivalent capacitance in series is always less than the smallest capacitance.

Step 3: Therefore, the correct relation is: \[ \boxed{\frac{1}{C_{\text{eq}}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}} \]