A network of capacitors is mostly inside a sealed box, but one capacitor C_X is sticking out, as shown in the figure. When you connect a multimeter across points a and b, it reads 27.0 µF. What is C_X? A) 27.0 µF B) 23.0 µF C) 4.0 µF D) 2.4 µF E) 2.2 µF

Question

Quizplus · Accepted Answer

When capacitors are in parallel, their total capacitance is the sum of their individual capacitances. Therefore, the capacitance of the network of capacitors inside the sealed box is the sum of all the capacitors except C_X. Let's call this total capacitance Ctotal. When C_X is connected in parallel with the network of capacitors, the total capacitance Ctotal+C_X is equal to the measured capacitance of 27.0 µF. Therefore, C_X can be calculated as: C_X = 27.0 µF - Ctotal We don't know the values of the other capacitors, but we can make an estimate based on the answer choices given. If C_X were 27.0 µF (choice A), then the total capacitance of the network would be 0 µF, which is impossible. If C_X were 23.0 µF (choice B), then the total capacitance of the network would be 4.0 µF, which is possible but unlikely since it would require the other capacitors to be very small. If C_X were 4.0 µF (choice C), then the total capacitance of the network would be 23.0 µF, which is a more reasonable value. If C_X were 2.4 µF (choice D) or 2.2 µF (choice E), then the total capacitance of the network would be even larger, which is unlikely. Therefore, the best choice is C: 4.0 µF.

A Network of Capacitors Is Mostly Inside a Sealed Box