In Fig. 25-18, a potential difference V=75.0 V is applied across a capacitor arrangement with c

step 1 we have been given a combination of capacitors. So two of which are in parallel with each other,

In Fig. 25-18, a potential difference V=75.0 V is applied...

In Fig. 25-18, a potential difference $V=75.0 \mathrm{~V}$ is applied across a capacitor arrangement with capacitances $C_{1}=10.0 \mu \mathrm{F}, C_{2}=5.00 \mu \mathrm{F}$, and $C_{3}=15.0 \mu \mathrm{F}$. What are (a) charge $q_{3}$, (b) potential difference $V_{3}$, and (c) stored energy $U_{3}$ for capacitor 3, (d) $q_{1}$, (e) $V_{1}$, and (f) $U_{1}$ for capacitor 1 , and (g) $q_{2}$, (h) $V_{2}$, and (i) $U_{2}$ for capacitor 2?

Key Concepts

Capacitors

A capacitor is an electrical component that stores energy in the form of an electric field, created by the separation of positive and negative charges on two conductive plates separated by an insulating material. Capacitors play a crucial role in circuits by filtering, timing, and energy storage.

Capacitance

Capacitance is a measure of a capacitor's ability to store charge per unit potential difference, expressed in farads (F). It is defined by the relationship Q = C × V, where Q is the charge stored, C is the capacitance, and V is the voltage across the capacitor.

Series and Parallel Combinations of Capacitors

Capacitors can be connected in series or parallel arrangements, which affect the overall charge distribution and voltage across each component. In series connections, the same charge appears on each capacitor and the total voltage is the sum of individual voltages, whereas in parallel connections, the voltage across each capacitor is the same and the total capacitance is the sum of the individual capacitances.

Charge-Voltage Relationship

The fundamental relationship between charge, capacitance, and voltage (Q = C × V) is used to determine one quantity when the other two are known. This concept is essential for analyzing circuits with capacitors, as it allows the calculation of the amount of charge stored or the voltage drop across any capacitor in the circuit.

Energy Stored in a Capacitor

The energy stored in a capacitor is given by the formula U = 1/2 C V^2, which highlights the dependence of energy storage on both the capacitance and the square of the voltage. This principle is used to determine the amount of energy that a capacitor can retain, which is important for applications involving energy storage and filtering in electrical circuits.

Transcript

00:01 We have been given a combination of capacitors.

00:04 So two of which are in parallel with each other, and then their equivalent capacitance is in series with the third one.

00:14 So there are three capacitors that have been given to us, and then they're connected to a voltage.

00:20 So we can say it's, let's say it's a source of voltage or battery.

00:23 And let me label all of them.

00:25 So this one is going to be c2.

00:27 This is c1 and this is c3.

00:30 And this is the voltage.

00:32 So here we have been given the following values so the voltage is given to us as 75 volts c1 is given to us as 10 micro -farrad c2 has been given to us as 5 mu f c3 has been given to us as 15 mu f.

00:54 Now we have to calculate there are around 7 to eight parts in this question and let's see how we can go about calculating each of them.

01:03 Now the first part, in the first part we have to find out the charge on the third capacitor.

01:12 So for that, firstly, the first step is always going to be finding out the equivalent capacitance.

01:18 So c equivalent here will be, so this part, c1 plus c2 because they're in parallel, it's going to give us 15.

01:25 So if i write down the equation directly, so it will be 15 into 15 upon 30, and this is going to give me 7 .5 mu f.

01:37 Now 7 .5 mu f is the equivalent capacitance of this entire, of this circuit.

01:44 Now let us find out how much charge is flowing in the entire circuit.

01:47 So for that, we know q is equal to cv.

01:50 So q equivalent, which is the total charge, will be c equivalent, which is 7 .5.

01:55 Into 10 raise to the power minus 6 into the voltage is given to us as 75.

02:01 Now on calculation we will get this value to be 5602 .5 mu c.

02:10 So this is the total equivalent charge of the entire in the entire circuit.

02:16 Now let us calculate the specific charge on q3.

02:21 And now we know since q3 is a part is a like a direct part of the, circuit we can directly say that q3 here will have the charge as the same charge as the equivalent charge because the charge flows this way so this entire combination over here will have the same charge as q3 so in this in case of c1 c2 it will get distributed but later again when it it will get recombined and c3 will have the charges 562 .5 no see now let's move on to the second part of the question.

02:58 So in the second part we are asked to find out the potential difference for c3...

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