A 4-μF capacitor is added in series with both capacitors shown in the circuit above. What is the ratio of the new equivalent capacitance to the original equivalent capacitance?

Question

A 4-μF capacitor is added in series with both capacitors shown in the circuit above.  What is the ratio of the new equivalent capacitance to the original equivalent capacitance?

Quizplus · Accepted Answer

11ecba2d_1301_0082_a3bf_e52d822a3fb5_MD0008_00 The 2-μF capacitors are connected in parallel because they are both connected to the same pair of wires. For capacitors connected in parallel, the equivalent circuit capacitance is the sum of the individual capacitances: 11ecba2d_1301_0083_a3bf_4f58e272d4de_MD0008_00 Therefore, the equivalent capacitance of the original circuit is: 11ecba2d_1301_0084_a3bf_95a59b0e2663_MD0008_00 For capacitors in series, the inverse of the equivalent capacitance is the sum of the inverses of the individual capacitances: 11ecba2d_1301_2795_a3bf_1d5a2fb89f19_MD0008_00 For capacitors in series, the circuit equivalent capacitance is always smaller than the smallest individual capacitance in the circuit. When the 4-μF capacitor is added in series with the given capacitor circuit, the equivalent capacitance of the new circuit is: 11ecba2d_1301_2796_a3bf_e9a9d847c072_MD0008_00 11ecba2d_1301_2797_a3bf_a394904afb07_MD0008_00 Therefore, the equivalent capacitance decreased to 2 from 4 μF, giving a new-to-original ratio of 1:2. (Choices A and D) If the equations for the equivalent capacitance in series and in parallel were switched, the original equivalent capacitance would be 1 μF, and the new equivalent capacitance would be 5 μF. Therefore, the new-to-original ratio would be calculated incorrectly as 5:1. (Choice C) If the 4-μF capacitor is placed in parallel with the other two resistors, the new equivalent capacitance would be 4 μF + 2 μF + 2 μF = 8 μF. Therefore, the new-to-original ratio would be calculated incorrectly as 2:1. Educational objective: For capacitors in parallel, the equivalent capacitance is the sum of the individual capacitances: 11ecba2d_1301_2798_a3bf_7505c0637365_MD0008_00 . For capacitors in series, the inverse of the equivalent capacitance is the sum of the inverses of the individual capacitances: 11ecba2d_1301_2799_a3bf_9ded2be71cd4_MD0008_00 .

A 4-μF Capacitor Is Added in Series with Both Capacitors