Consider three capacitors c1 c2 and c3 and a battery if only...

Consider three capacitors C1, C2, and C3 and a battery. If only C1 is connected to the battery, the charge on C1 is 32.0 µC. Now C1 is disconnected, discharged, and connected in series with C2. When the series combination of C2 and C1 is connected across the battery, the charge on C1 is 22.2 µC. The circuit is disconnected, and both capacitors are discharged. Next, C3, C1, and the battery are connected in series, resulting in a charge on C1 of 25.4 µC. If, after being disconnected and discharged, C1, C2, and C3 are connected in series with one another and with the battery, what is the charge on C1 in µC?

Transcript

0:00 Hi.

00:01 Here in this given problem there are three capacitors, three different capacitors which are having capacitance c1, c2 and c3 and a battery providing a voltage, suppose e.

00:45 There are three different situations.

01:04 In the first one, only first capacitor is joined along the battery.

01:11 The first capacitor having capacitance c1, in battery having potential e.

01:19 The second condition in which the two capacitors c1 and c2 are joined in series with the same battery.

01:35 The third condition, the two capacitors c1 and c3 are joined in series now with the same battery.

01:57 And last, in which all three are joined in series with the same battery.

02:07 And before each connection, the respective capacitors are disconnected from the previous circuit and then discharged and then joined again in series with the different capacitors.

02:25 Now for the first case here we can mark them as the first one, the second one, the third one and the fourth one.

02:38 So in the first case, charge passing through capacitor c1, expression for the charge charge is given as q is equal to c into v.

02:50 For c this is c1 for v this is e only and the charge is given as 32 micropula.

02:57 Make it equation number 1.

03:00 Then this was for the case 1.

03:07 Then for case 2, this time c1 and c2 are in series and the charge passing through them q2.

03:21 Net capacitance of two capacitors in series combination will be c1 into c2 divided by c1 plus c2 into e and this charge is given as 22 .2 microculum charge passing through capacitor c1 again but as in series charge remains the same.

03:42 So the net charge passing through the branch passing through this arm will be the charge passing through c1 also.

03:50 Then for case 3 this time the charge is q3, net capacitance is c1 into c3 divided by c1 plus c3 battery having the same potential e.

04:08 And this charge is given as 25 .4 microcule.

04:13 Make it equation number 3.

04:16 Now what do we do? we divide equation 2 by equation 1.

04:23 So we will get c2 by c1 plus c2 is equal to 22 .2 divided by 32.

04:34 Making a cross multiplication, we get 22 .2c1 plus 22 .2c2 is equal to 32c2...