Find the charge on each of the capacitors in Figure P 16.43...

Name: Problem 43, Chapter 16: College Physics
Uploaded: 2021-06-05T22:22:04-08:00
Duration: 11 min 40 s
Channel: Linda Winkler
Description: Find the charge on each of the capacitors in Figure P 16.43

Key Concepts

Voltage Division

Voltage division refers to the way the total voltage of a circuit is apportioned across components, particularly in series circuits. For capacitors in series, each capacitor experiences a fraction of the total voltage, and this division is influenced by the individual capacitances. Mastery of this concept is key to determining the charge on each capacitor, since the charge is related to the voltage across each component.

Equivalent Capacitance

Equivalent capacitance is a concept used to simplify a network of capacitors to a single capacitor that has the same effect on the overall circuit. In series, the reciprocals of the capacitances add up, and in parallel, the capacitances add directly. This simplification helps in calculating the overall charge and voltage distribution in the circuit.

Capacitance

Capacitance is the ability of a capacitor to store electric charge per unit voltage, defined by the relation Q = CV, where Q is the charge stored, C is the capacitance, and V is the voltage across the capacitor. It is a fundamental property that determines how much charge a capacitor can store for a given applied voltage.

Series and Parallel Configurations

In electrical circuits, capacitors can be connected in series or in parallel. In series configurations, the same charge flows through each capacitor while the voltage divides among them; in parallel configurations, the voltage across each capacitor is the same while the total charge stored is the sum of the charges on individual capacitors. Understanding these configurations is essential for analyzing complex circuits.

Transcript

00:01 Here, we're going to use the ideas of series and parallel capacitance in order to determine the amount of charge on each of the four capacitors inside of this circuit, which is hooked up to a 24 -volt battery.

00:21 And so the ideas that we'll use is series means same charge.

00:28 So there is no other path for the charge to distribute itself upon.

00:39 And so all plates will be lined up in a stack with alternating plus minus charge of the same amount.

00:48 Parallel means same voltage difference.

00:58 So that is a conservation of energy argument.

01:10 And typically what that means is that two components.

01:13 In parallel are sharing the same endpoints.

01:20 So you can think about voltage as being like a hill.

01:24 And so you're looking at two components that share the same top of the hill and the same bottom of the hill.

01:32 So if we look at the circuit with the four capacitors, what we note is that the top two capacitors that i've shown in green share the same end points.

01:45 So they are in parallel.

01:48 And the way you calculate capacitance in parallel is simply by adding the individual capacitance inside of the parallel arrangement.

02:03 In this case, we're going to add c1 and c2 for that green configuration.

02:09 And that will give us six micro -faradays.

02:16 And the bottom, arrangement is also in parallel.

02:21 Again, those two capacitors share the same endpoints, top and bottom.

02:28 So that is also a parallel arrangement.

02:32 I've called cpb, and again, we'll just add c3 and c4.

02:44 And that gives us 12 microfaradays.

02:50 And i should point out that the series calculation is a little bit trickier.

02:57 You have to add inverses of capacitancees, and we don't have any such arrangement, but let's say there was a c5 and a c6.

03:13 We'll just make up some numbers, so you recognize we're not doing that with these capacitors, but you would add inverses and then take the inverse.

03:27 So we can redraw the circuit, and i will do that.

03:33 We have a 24 -volt battery, and now we can imagine that simplified down to a top capacitance of 6 micro -faradays and a bottom capacitance of 12 ferrides.

03:55 So this is the idea of reducing a circuit to a simpler configuration in order to find out individual pieces of information that you're interested in.

04:09 And i see that these two are in series, and i could determine the series capacitance, and i probably should reduce this down into one more simplified circuit.

04:34 So here my c -series, i would add the inverses of those two over six micro -ferodys, plus 1 over 12 micro -ferridaes.

04:50 And then don't forget to invert that one more time.

04:55 And we would get something fairly simple for micro -fairdays.

05:18 Okay, so we can simplify the circuit down into a much simpler picture.

05:26 A single battery of 24 volts with a 4 -micro -faraday capacitor...

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