A capacitor of 10 F is connected in parallel with a series combination of two identical capacitors, each of capacitance C . If the equivalent capacitance of the entire arrangement is 14 F , what is the value of C ?

Step-by-step solution

Let the equivalent capacitance of the two identical capacitors in series be C_s . Since they are in series, C_s = C C C + C = C 2 . This series combination is connected in parallel with a 10 F capacitor. The equivalent capacitance of the entire arrangement is given as 14 F . For a parallel combination, the equivalent capacitance is the sum of the individual capacitances: C_ eq = 10 F + C_s Substituting the given values: 14 F = 10 F + C 2 C 2 = 14 F - 10 F = 4 F C = 8 F Answer: 8 F