Two capacitors are connected in parallel as shown above. A voltage V is applied to the pair. What is the ratio of charge stored on C1 to the charge stored on C2, when C1 = 1.5C2 ?
how do you do this? ( The answer is 3/2)
Thanks for helping ; ) I appreciate that
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This is the figure...
Capacitors in parallel have the same voltage V applied to each.
The stored charge on each is CV.
Since V is the same the ratio of charges is the ratio of capacitances, C.
Q1/Q2 = C1/C2 = 1.5
To solve this problem, we need to understand that in a parallel connection, the voltage across each capacitor is the same, but the charges stored on each capacitor may vary.
Let's assume that the charge stored on capacitor C1 is Q1 and the charge stored on capacitor C2 is Q2.
Given that C1 is 1.5 times C2, we can express this as:
C1 = 1.5C2
The formula for the charge stored on a capacitor is:
Q = CV
Where Q is the charge stored, C is the capacitance, and V is the voltage applied.
For capacitor C1, the charge stored is Q1 = C1V.
For capacitor C2, the charge stored is Q2 = C2V.
Since the voltage V is the same for both capacitors, we can write:
Q1/Q2 = (C1V)/(C2V)
Simplifying this equation using the given relationship C1 = 1.5C2, we have:
Q1/Q2 = (1.5C2V)/(C2V)
Q1/Q2 = 1.5/1
Q1/Q2 = 3/2
Therefore, the ratio of the charge stored on C1 to the charge stored on C2 is 3/2.
To find the ratio of charge stored on C1 to the charge stored on C2, we'll use the fact that the charge stored is proportional to the capacitance. Therefore, the ratio of the charge stored on C1 to the charge stored on C2 will be equal to the ratio of their respective capacitance values.
Given that C1 = 1.5C2, we can write this equation as:
Charge on C1 / Charge on C2 = C1 / C2 = 1.5 / 1
This simplifies to:
Charge on C1 / Charge on C2 = 3/2
So, the ratio of the charge stored on C1 to the charge stored on C2 is 3/2.