Question

Four condensers each of capacitance 8 muF are joined as shown in the figure. The equivalent capacitance between the points A and B will be
 

• A. 32 μF
• B. 2 μF
• C. 8 μF
• D. 16 μF

Hint:

In mixed combinations of capacitors (series and parallel), first find the equivalent capacitance of the series combination and then find the total capacitance of the parallel combination.

Answer 1

The Correct Option is A

We are given four capacitors, each of capacitance \( 8 \ \mu F \), connected as shown in the diagram. We need to calculate the equivalent capacitance between points A and B. 

Step 1: Identifying the Capacitor Connections 
From the figure: - The top two capacitors are in series. - The bottom two capacitors are also in series. - These two series combinations are in parallel with each other. 

Step 2: Capacitance of Each Series Pair 
The capacitance of two capacitors in series is given by: \[ \frac{1}{C_{\text{series}}} = \frac{1}{C} + \frac{1}{C} \] Since each capacitor has capacitance \( 8 \ \mu F \), \[ \frac{1}{C_{\text{series}}} = \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4} \] Thus, \[ C_{\text{series}} = 4 \ \mu F \] Step 3: Equivalent Capacitance of Parallel Combination 
The two series combinations are now in parallel. For capacitors in parallel: \[ C_{\text{eq}} = C_{\text{series}} + C_{\text{series}} \] \[ C_{\text{eq}} = 4 \ \mu F + 4 \ \mu F = 8 \ \mu F \] 

Step 4: Final Equivalent Capacitance 
Notice that this combination is in parallel with another identical combination of capacitors (from symmetry in the diagram). The total equivalent capacitance is: \[ C_{\text{total}} = 8 \ \mu F + 8 \ \mu F = 32 \ \mu F \]

 Step 5: Final Answer 
\[ \boxed{32 \ \mu F} \]