Question

The total capacitance across points 1 and 2 in the circuit shown is

• A. \(0.66\,\mu F\)
• B. \(4.66\,\mu F\)
• C. \(3.66\,\mu F\)
• D. \(2.66\,\mu F\)

Hint:

Always reduce complex capacitor networks step-by-step.

Answer 1

The Correct Option is D

Concept: Capacitors in:

• Series: \(\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2}\)

• Parallel: \(C = C_1 + C_2\)

Step 1: Identify network The circuit consists of a bridge-like arrangement of \(1\mu F\) capacitors.

Step 2: Combine vertical capacitors Two vertical capacitors are in parallel: \[ C = 1 + 1 = 2\mu F \]

Step 3: Combine series with bottom branch Series with another \(1\mu F\): \[ \frac{1}{C} = \frac{1}{2} + \frac{1}{1} = \frac{3}{2} \Rightarrow C = \frac{2}{3}\mu F \]

Step 4: Add remaining parallel branch Add with another \(2\mu F\): \[ C_{eq} = 2 + \frac{2}{3} = \frac{8}{3} = 2.66\mu F \]

Step 5: Final Answer \[ \boxed{2.66\,\mu F} \]