Capacitors in Parallel: Finding the Relationship Between Capacitance and Charge

[Tanishq Nandan]

Homework Statement

Two capacitors C1 and C2 are charged to 120V and 200V respectively.It is found that on connecting them together the potential on each one of them can be made zero.Then,
A)3C1=5C2
B)3C1 + 5C2=0
C)9C1=4C2
D)5C1=3C2

Homework Equations

Q=CV
Q-charge on capacitor
C-capacitance
V-potential diff across plates
Capacitors in parallel have same potential difference

The Attempt at a Solution

After charging the capacitors to their respective voltages,the charges on them are:
On C1: 120C1 and -120C1
On C2: 200C2 and -200C2
Now,when we connect them in parallel,according to question,potential across them becomes zero.
Through Q=CV,
if V=0,Q=0 as well...
So there's no charge on any capacitor

So,the total charge on them ought to be zero..i.e..120C1+200C2=0
Option B
But,the answer given is A.
I think..maybe my assumption of "connecting them together" in the question as a parallel configuration is wrong..maybe something else..

 

[berkeman]

The problem with answer B is that the sign is wrong. If it were B)3C1 - 5C2=0 then it would be correct, and the same as answer A.

The Q in Q=CV is the same polarity as CV. The reverse polarity comes because of the way the two capacitors are connected to cancel out the net charge. Does that make sense?

 

[ehild]

1

So,the total charge on them ought to be zero..i.e..120C1+200C2=0
Option B
But,the answer given is A.
I think..maybe my assumption of "connecting them together" in the question as a parallel configuration is wrong..maybe something else..

The capacitance is defined as non-negative. You can connect the capacitors positive side with positive side, and positive side with negative side as @berkeman suggested.

 

[Tanishq Nandan]

The reverse polarity comes because of the way the two capacitors are connected to cancel out the net charge

Which way are the capacitors connected?that's my entire problem..

You can connect the capacitors positive side with positive side, and positive side with negative side

Well,wouldn't the two cases give two different answers?
Positive with positive would mean 120C1+200C2 is 0
Positive with negative would mean 120C1 +(-200C2) is 0

 

[ehild]

Which way are the capacitors connected?that's my entire problem..Well,wouldn't the two cases give two different answers?
Positive with positive would mean 120C1+200C2 is 0
Positive with negative would mean 120C1 +(-200C2) is 0

C1 and C2 are capacitances, never negative. So connecting the plates of the capacitors positive to positive, negative to negative, the overall potential difference between the plates can not be zero.

 

[Merlin3189]

After charging the capacitors to their respective voltages,the charges on them are:
On C1: 120C1 and -120C1
On C2: 200C2 and -200C2
Now,when we connect them in parallel,according to question,potential across them becomes zero.
Through Q=CV,
if V=0,Q=0 as well...
So there's no charge on any capacitor

So,the total charge on them ought to be zero..i.e..120C1+200C2=0

Arguing intuitively gives the correct answer a) and not b)
But following through with your math, the two possible situations are
Q1 = 120C1 and Q2= -200C2 or
Q1=-120C1 and Q2=200C2
neither of the other combinations can give zero when added

so the toatal charge is Q1 + Q2 = 0, ie. 120C1 - 200C2 = 0 or -120C1 +200C2 = 0 , both giving a) but not b)

 

[Tanishq Nandan]

Okk,I get it now.Thanks ppl !