A 100 pF capacitor is charged to a potential difference of 80.0 V, and the charging battery is

A 100 pF capacitor is charged to a potential difference of...

A $100 \mathrm{pF}$ capacitor is charged to a potential difference of $80.0 \mathrm{~V}$, and the charging battery is disconnected. The capacitor is then connected in parallel with a second (initially uncharged) capacitor. If the potential difference across the first capacitor drops to $35.0 \mathrm{~V}$, what is the capacitance of this second capacitor?

Key Concepts

Charge Conservation

In an isolated system, the total electric charge is conserved. When components such as capacitors are connected and allowed to exchange charge, the initial total charge remains constant. This principle is used to equate the sum of charges before and after capacitors are connected.

Capacitor

A capacitor is an electrical component that stores energy in the electric field between its plates and is defined by its capacitance, which relates the stored charge to the voltage across its plates using the relation Q = CV. This fundamental relationship is key to analyzing charge and voltage in circuits.

Capacitors in Parallel

When capacitors are connected in parallel, they share the same voltage across their terminals. This characteristic allows for the redistribution of charge between them while maintaining voltage equality, and is essential when calculating the final voltages and determining unknown capacitances in circuit analysis.

Transcript

00:01 In this question we've been initially given a capacitor c1 which has a capacitance of 100 picofarrets and it is given that it is charged using a battery of 80 volts and so let's find out first how much charge is accumulated on this capacitor so q1 becomes c1 v1 and c is 100 into 10 ratios of a minus 12 and v is 80 so this can be finally written as 8 nanoculums.

00:34 This is the charge how much it has been able to accumulate after charging with the 80 volts battery.

00:40 Now this charging battery is disconnected and it now this this c1 capacitor is connected with another uncharged capacitor.

00:50 So let's say this is c1 and this is another capacitor c2.

00:55 Now what happens is that since this is uncharged there is high potential difference between both of them so the charges start flowing from c1 to c2 and this charge this charge flow of charge takes place until the potential does not become same so as then when the potential becomes same the the flow of charges stops so let's see how we can write this so since both of them are connected in parallel we can say that the potential drop across both of them is equal so now we can say that the charge flowing to the first capacitor will be c1 into v.

01:32 Now v dash is given to us as 35 volts.

01:36 So after while the in this entire process of charging the potential of c1 drops to 35 so the new potential is given to us as 35 so c1 is 100 into 10 raised to the power minus 12 and v dash is given to us as 35 so this becomes 3 .5 nanoculums.

01:59 This is a new charge of the first capacitor.

02:04 Now we know since this was the total charge, so whatever the remaining charge is, it has gone to the second capacitor...

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