Two capacitors of capacitance 2 F and 4 F are connected in parallel. This combination is then connected in series with an unknown capacitor C₃ . If the total equivalent capacitance of the entire arrangement is 3 F , what is the value of C₃ ?

Step-by-step solution

The equivalent capacitance of the two capacitors in parallel is: C_p = 2 F + 4 F = 6 F This combination C_p is in series with C₃ . The total equivalent capacitance C_ eq is given as 3 F . For capacitors in series, the formula is: 1 C_ eq = 1 C_p + 1 C₃ Substituting the known values: 1 3 = 1 6 + 1 C₃ 1 C₃ = 1 3 - 1 6 = 2 - 1 6 = 1 6 Therefore, C₃ = 6 F . Using the formula C_ eq = C_p C₃ C_p + C₃ incorrectly to solve for C₃ as if it were the equivalent of 3 and 6 in series leads to the wrong answer of 2 F . Answer: 6