{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CourseNotes.25

# CourseNotes.25 - K 3 is q = K 3 V = 3 C 5 V Stepping back...

This preview shows page 1. Sign up to view the full content.

Figure 20: An Arrangement of Capacitors Capacitor 2 is not as easy however. We will find the charge on capacitor 2 in the usual manner, by working the circuit down to its simplest form and then working back out. Before we start simplifying, we will note that the upper portion of the circuit plays no role in the bottom portion and we will therefore ignore it all together. The idea behind simplifying a circuit is to look for pairs of capacitors that are wired either in series or in parallel. The first pair that we will simplify is C 2 and the other capacitor on the same wire as C 2 . Since they are in parallel, K 1 = 1 1 C + 1 C = C 2 where we are using K to denote an imaginary equivalent capacitor. We can now treat this equivalent capacitor as being in parallel with the one which is nearest to it. K 2 = C 2 + C = 3 C 2 And finally, this equivalent capacitor is in series with the fourth capacitor in the lower portion of the circuit. K 3 = 1 1 C + 2 3 C = 3 C 5 We are now ready to step our way back out to the answer. The charge on
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: K 3 is q = K 3 V = 3 C 5 V Stepping back one more level, K 2 and the other capacitor are in series and must therefore have the same charge. Hence, q = 3 C 5 V . We can use this information to calculate the voltage across K 2 . V = q K 2 = 3 C 5 2 3 C V = 2 5 V Stepping back another level, K 1 and C are now in parallel and must therefore have the same voltage diﬀerence. Using this to ﬁnd the charge gives. q = K 1 V = C 2 2 5 V = CV 5 Finally, since K 1 is made up of two capacitors in series (one of which is C 2 ), the charge must be that same on both. The charge on C 2 is therefore q 2 = CV 5 = 2 × 10-5 C Problem 25.64 The capacitances of the four capacitors shown in ﬁgure 21 are given in terms of a certain quantity C . (a) If C = 50 μF , what is the equivalent capacitance between points A and B ? (b) Repeat for point A and D . 25...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern