Question

In a parallel bridge circuit involving capacitors, the circuit's resultant capacitance is to be determined. If the capacitance values are given, calculate the resultant capacitance in the parallel combination. Assume the capacitors have the following capacitance values:
\( C_1 = 2 \, \mu\text{F} \) 
\( C_2 = 3 \, \mu\text{F} \)
\( C_3 = 4 \, \mu\text{F} \)

The capacitors are connected in parallel.

• A. \( C_{\text{eq}} = 9 \, \mu\text{F} \)
• B. \( C_{\text{eq}} = 6 \, \mu\text{F} \)
• C. \( C_{\text{eq}} = 5 \, \mu\text{F} \)
• D. \( C_{\text{eq}} = 7 \, \mu\text{F} \)

Hint:

For capacitors in parallel, always add the individual capacitances to find the total or resultant capacitance. This is different from series combinations where the reciprocal sum is used.

Answer 1

The Correct Option is A

For capacitors in parallel, the equivalent capacitance \( C_{\text{eq}} \) is the sum of the individual capacitances: \[ C_{\text{eq}} = C_1 + C_2 + C_3 \] Substitute the given values: \[ C_{\text{eq}} = 2 \, \mu\text{F} + 3 \, \mu\text{F} + 4 \, \mu\text{F} \] \[ C_{\text{eq}} = 9 \, \mu\text{F} \] Thus, the resultant capacitance of the parallel combination is \( 9 \, \mu\text{F} \).