Imagine two capacitors with difference capacitance connected in series across a
ID: 2236671 • Letter: I
Question
Imagine two capacitors with difference capacitance connected in series across a battery. a) Do the two capacitors have the same amount of charge on each of their plates? Is the potential difference between the plates of each capacitor the same? b) How are the two capacitors like a single capacitor? Could you replace the two capacitors with a single capacitor? If so, what would be the potential difference across the replacement capacitor in terms of the potential differences across each of the original capacitors? Write this in terms of an equation. c) Use the equation that relates the potential difference on the new capacitor the potential differences V1 and V2 and the relationship between charge and potential difference for each capacitor to find the capacitance of the replacement capacitor in terms of the capacitances C1 and C2 of the original two capacitors.Explanation / Answer
a)They have the same charge.
The potential difference between plates is not the same.
b)Yes, they can be replaced by a single capacitor.
Since they have the same charge,
the following equation for total voltage across them holds.
Vtot=V1+V2=Veq
c)Q/C1+Q/C2=Q/Ceq
Dividing by Q,
1/C1+1/C2=1/Ceq
Ceq=C1C2/(C1+C2)