The circuit below shows three capacitors in a circuit...

The circuit below shows three capacitors in a circuit connected to a battery. The capacitances are C₁ = 2.51F, C₂ = 3.51F, and C₃ = 2.61F. a) What is the equivalent capacitance of the three capacitors? Give your answer in F. b) The battery has a voltage of V = 20 volts. What is the charge stored on the equivalent capacitor? c) If this amount of charge is also on capacitor C₁, what is the voltage across this capacitor?

Transcript

00:01 Hello students so in this question we have the following circuit consisting of various capacitors connected across a 12 volt battery so first question is that we need to find out the net capacitance of the circuit so we can see that capacitors c2 and c3 are connected in series are connected in series so we have if c does is the net capacitance of c2 and c3 connected in series then c dash is equal so 1 by c dash would be equal to 1 by c2 plus 1 by c3 or we have c dash is equal to c2 multiplied by c3 divided by c2 plus c3 so putting all the values we get c2 multiplied by c3 is 2 .39 multiplied by 4 .07 divided by 2 .39 plus 4 .07 micro ferrard on making this calculation we get the value of c dash to be equal to 1 .506 micro ferrad and this cdass capacitor is then connected in parallel to the c1 capacitor so we have cdass and c1 are parallel to each other are parallel to each other so we have the net capacitance of the circuit is equal to c1 plus c that is equal to 1 .506 plus the value of c1 we have is equal to 4 .86 micro ferret and this is equal to 6 .36 .36 micro ferret so this is the value of net capacitance of the circuit now we'll move on to the second part of the question so it's part b so in the second part of the question we have are asked to find out what is the net energy stored in the circuit so we'll find out the energy stored in the circuit in the circuit is u is equal to half c net v square so it's 1 by 2 multiplied by 6 .366 multiplied by 10 to the power minus 6 multiplied by 12 whole square in jules so if we make this calculation we get the total energy stored in the capacity is equal to 1 by 2 multiplied point 6 .366 multiplied by 10 to the power minus minus multiplied by 144 this is in jules and this we get to be equal to 458 0352 multiplied by 10 to the power minus 6 twos.

03:39 So this is the total amount of energies that is stored in the circuit.

03:45 Now we will move on to the third part of the question.

03:50 So in the third part of the question, we are asked to find out what is the net voltage across each of the capacitor? the net voltage across each of the capacitor, then we note that the voltage across capacitor capacitor c1 is equal to 12 volts and that is very evident from the it is very evident from the figure here that c1 the voltage across c1 is this the voltage across this two again points that is 12 volt similarly if the net capacitance of c2 and c3 connected in c c dash then the net voltage across c dash is also equal to 12 volts so we can write that similarly we can say that the voltage across c dash is also equal to 12 volts is also equal to 12 volts so we can say the total charge on c dash the total charge on c dash is equal to how much that will be equal to q dash is equal to cdash multiplied by v so we have q dash is equal to 12 multiplied by the value of c dash here and the value of c we got to be equal to 1 .506 microferat 1 .506 microferat this will be in micro cool up so we get the value of q dash to be equal to 18 .070 to microculeum so this is the total charge on c dash which is the net capacitance of c2 and c3 which are present in series now since both these capacitors are present are connected to each other in series so we can say that the total charge the total charge on c2 is equal to the total charge on c3 and this is equal to q dash that is equal to 18 .072 this is the total charge on c2 and this is a total charge on c3.

06:45 So we can say that q2, that is the charge and capacitor, c2 is equal to 18 .072 microculum and q3, which is the charge on capacitor 3 is equal to 18 .072 microculum...

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