Capacitors in Parallel: Finding the Relationship Between Capacitance and Charge

In summary, two capacitors C1 and C2 are charged to 120V and 200V respectively. When connected together, the potential on each capacitor can be made zero. The question asks for the relationship between the two capacitances, and the correct answer is A)3C1=5C2. This is because when the capacitors are connected in parallel, the total charge on them must be zero, leading to the equation 120C1-200C2=0. The incorrect answer B)3C1+5C2=0 has the wrong sign and does not account for the way the capacitors are connected to cancel out the net charge.
  • #1
Tanishq Nandan
122
5

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..
 
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  • #2
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?
 
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  • #3
Tanishq Nandan said:
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.
 
  • #4
berkeman said:
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..

ehild said:
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
 
  • #5
Tanishq Nandan said:
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.
 
  • #6
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)
 
  • #7
Okk,I get it now.Thanks ppl !
 

Related to Capacitors in Parallel: Finding the Relationship Between Capacitance and Charge

What is the purpose of connecting capacitors in parallel?

The purpose of connecting capacitors in parallel is to increase the total capacitance in a circuit. This allows for more charge to be stored and released, providing a larger amount of energy to the circuit.

How do capacitors in parallel affect the overall capacitance?

When capacitors are connected in parallel, their individual capacitances add up to create a larger overall capacitance. This is because the total charge stored in the circuit is the sum of the charges stored on each capacitor.

What happens to the voltage across each capacitor when they are connected in parallel?

When capacitors are connected in parallel, the voltage across each capacitor remains the same. This is because the voltage drop across each capacitor is equal to the voltage of the circuit.

Can capacitors in parallel be replaced by a single equivalent capacitor?

Yes, capacitors in parallel can be replaced by a single equivalent capacitor with a capacitance value equal to the sum of the individual capacitors' values. This is known as the equivalent capacitance.

What is the effect of having different capacitance values when connecting capacitors in parallel?

When connecting capacitors in parallel with different capacitance values, the total capacitance will be equal to the sum of the individual capacitances. However, the charge and energy stored in each capacitor may be different.

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