In Fig. 25-28, a potential difference V=100 V is applied across a capacitor arrangement with ca

In Fig. 25-28, a potential difference V=100 V is applied...

Key Concepts

Charge Conservation and Distribution

Charge conservation principles ensure that in a closed circuit, the total charge is conserved. In capacitor networks, especially in series configurations, the same charge appears on each capacitor, which directly affects the voltage distribution and energy stored in each element.

Energy Storage in Capacitors

The energy stored in a capacitor is given by the formula U = ½CV². This relationship shows that the energy is a function of both the capacitance and the square of the voltage across it, and is essential when analyzing how much work a capacitor can perform or how much energy it holds.

Voltage Division in Series Circuits

In a series configuration, the applied voltage is divided among the capacitors in proportion to the inverse of their capacitances. This principle allows one to determine the voltage drop across each capacitor based on its individual capacitance relative to the entire series combination.

Series and Parallel Configurations

Capacitors can be connected in series or parallel within a circuit. In series connections, the same charge flows through each capacitor and the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances. In parallel, the voltage across each capacitor is identical and the total capacitance is the sum of the individual capacitances.

Capacitance and Q=CV Relationship

Capacitance is a measure of a capacitor's ability to store electrical charge per unit potential difference. The direct relationship Q = CV, where Q is the charge, C is the capacitance, and V is the voltage, is fundamental in determining the stored charge given any applied voltage.

Equivalent Capacitance Calculation

Calculating the equivalent capacitance of a capacitor network simplifies complex circuit analysis by reducing multiple elements into a single effective capacitor. This process differs between series and parallel arrangements and is key to determining overall circuit behavior such as the distribution of voltage and stored energy.

Transcript

0:00 Hi there.

00:01 So for this problem, we are given the figure that is shown in here.

00:05 And it is a circuit with a potential difference b, which is equal to 100 poles.

00:17 And it is applied to across these capacitors.

00:21 And we are given the information about the capacitance of each of these capacitors.

00:26 So for c1, we have 10 micropharmatores.

00:30 For the capacitance 2, we have 5 micropharets.

00:38 And for the capacity 3, we have 4 microphorets.

00:48 And what we need to obtain for the first part of this problem is the charge of the capacitor 3, which we call q3.

01:01 Now, in order to obtain that, we know that the charge in the figure, the voltage in that capacitor is simply the potential difference that is applied to these capacitors.

01:19 So we just need to simply use our equation for the charge.

01:23 We know that the charge is equal to the product between the capacitance of the capacitor times the potential difference.

01:31 So we have these two values.

01:32 We know that the capacitance is four micro -fares times.

01:38 Times 100 bulls.

01:41 Remember that micro means 10 to the minus 6.

01:47 So substituting that into the calculator, we obtained that the charge q3 is 4 times 10 to the minus 4 columns.

01:57 So this is a solution for the first part of this problem.

02:02 Now for part b, we are asked about the potential difference in b3.

02:14 So that is the potential difference in the capacitor 3.

02:19 But as you can see, since this is in parallel to the other capacitors, and at the same time with the voltage, we will have that this potential difference is the same as the potential difference that is applied to all of these capacitors, which is 100 volts.

02:41 So this is a solution for part b of this problem.

02:46 Now for part c, we are asked about the stored energy for the capacitor 3.

02:54 So we call this u3, that is store energy.

02:58 We know that the store energy is equal to one half of the capacitance times the voltage, in that capacitor.

03:12 Now, in this case, we will have that for the capacitor 3, we will have that that is one half of the capacitance 3 of this capacitor, and its voltage, which is b3 squared.

03:26 So we need to simply substitute all those values.

03:29 We know that the capacitance of this capacitor is for micro -forets.

03:35 The voltage is 100 volts.

03:39 To the squared.

03:41 So plotting this into the calculator we obtained that the energy stored on that capacitor is equal to 2 times 10 to the minus 2 joules...

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