In Fig. 25-19, a potential difference V=100 V is applied across a capacitor arrangement with ca

In Fig. 25-19, a potential difference V=100 V is applied...

Key Concepts

Capacitance

Capacitance is a measure of a capacitor's ability to store electric charge per unit voltage, defined by the relationship Q = CV, where Q is the charge stored, C is the capacitance, and V is the voltage. This concept is fundamental in analyzing how individual capacitors behave in a circuit when connected to a voltage source.

Series and Parallel Capacitor Configurations

Capacitors can be arranged in series or parallel, and the configuration determines how voltage and charge distribute among them. In a series arrangement, the same charge passes through each capacitor while the voltage divides inversely with capacitance, whereas in a parallel configuration, all capacitors experience the same voltage across their terminals and the total stored charge is the sum of the individual charges.

Equivalent Capacitance

The equivalent capacitance of a circuit is a single capacitance that can replace a combination of multiple capacitors without changing the overall behavior of the circuit. In series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances, while in parallel, the equivalent capacitance is obtained by directly summing up all individual capacitances. This simplification allows easier analysis of complex circuits.

Charge-Voltage Relationship

The direct relationship between charge and voltage for a capacitor, expressed as Q = CV, is crucial when determining how much charge is stored on each capacitor for a given applied voltage. Understanding this relationship helps in calculating the distribution of charge in various circuit configurations.

Voltage Division

Voltage division refers to the distribution of the applied potential difference across different components within a circuit. For capacitors in series, the voltage across each capacitor is determined by its capacitance relative to the other capacitors in the series, ensuring that the sum of these voltage drops equals the total applied voltage.

Energy Storage

The energy stored in a capacitor is given by the formula U = ½ CV², which shows that the energy depends on both the capacitance and the square of the voltage across the capacitor. This concept is essential for understanding the energy dynamics in circuits involving capacitors, especially when comparing energy storage in different configurations.

Transcript

00:01 This question we have been given the circuit and i'll be drawing the circuit over here.

00:05 So in this circuit this is an overall parallel circuit but it has a component, it has one component which is series inside.

00:16 And then this is connected to a potential drop of v.

00:20 Now let us label this.

00:22 So the capacitor, this one is c3.

00:27 The one below is c1 and this is c2.

00:29 Now let us write down the values.

00:32 So c1 is given to us as 10 mu f, c2 is given to us as 5 mu f, c3 is given to us as 2 mu f, and the voltage, the potential drop, is given to us as 100 volts.

00:48 Now we have to calculate approximately 7 to 8 parts or i guess more than that in this question.

00:55 So let's see how we'll go about by calculating each of the parts.

01:00 So in the first part which is part a, we have to calculate charge on the third capacitor which is c3 and it's given as q3.

01:11 Now firstly in this we need to understand the combination of the circuit over here.

01:19 So whenever two components are connected in parallel to each other, the entire parallel connection will have the same voltage.

01:28 So even c1 plus c2 combined will have the same voltage as v whereas even c3 will have the same voltage.

01:36 So q3 we know the formula for chart so q3 is equal to c3 v3.

01:43 So c3 is given to us as 2 into 10 raise to the power minus 6 and v3 here will be 100.

01:50 Because this in parallel the potential difference remains same for both the branches which even the upper one as well as the lower one.

01:58 So this can be written as further 200 microculems.

02:04 So this is the charge on the third capacitor.

02:07 Let us move on to the second part of the question.

02:10 In the second part we've been asked to find out the potential difference across the third capacitor which is v3.

02:17 Now v3 can simply be written as 100 volts because we have calculated.

02:22 We have found out the logic earlier as well.

02:26 Now let us move on to the third part of the question.

02:28 Which is part c now in this part they have asked us to find out the energy stored in the third capacitor which is u3 so let's see how we can do this so we know u3 is equal to half cv c3 v3 square so in this half we we can write it as half into c3 is 2 into 10 x to the power minus 6 and v3 is 100 squared so this on calculation we will get the answer to be as 10 raised to the power minus 2 joules.

03:03 So this is the energy stored in the third capacitor.

03:07 Now let's move on to the fourth part of the question, which is part d.

03:11 In this part we are asked to find out q1, which is the charge on the first capacitor.

03:17 So for this we need to now go into slightly depth.

03:22 We know that the charge which is flowing through the third capacitor, q3, is 200.

03:31 Microculums.

03:32 And now we have to find out what will be the charge flowing through q1.

03:37 So if we if we can find out the total charge and then subtract q3 from it, we will get the charge which is going through this branch where c1 is present.

03:47 So let's see how we can calculate the total charge.

03:50 So total charge in the circuit will be equivalent capacitance into the total voltage potential difference...

Please give Ace some feedback