
A capacitor is charged up to a voltage by connecting it to a battery through the switch . Now is disconnected from battery and connected to a circuit consisting of two uncharged capacitors and through a switch as shown in the figure. The sum of final charges an and is:
(A)
(B)
(C)
(D)

Answer
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Hint: The sum of the final charges an and can be determined by using two formulas. The capacitor is series formula and then the potential difference in capacitor formula. By using the given information in these two formulas, the sum of final charges and can be determined.
Formulae Used:
Capacitor in series,
Where, is the equivalent capacitance, capacitance of the first capacitor and is the capacitance of the second capacitor.
Potential difference in capacitor,
Where, is the potential difference, is the charge and is the capacitance.
Complete step-by-step solution:
Given that,
A capacitor,
Voltage
The capacitance is, and
Capacitor in series, and the capacitors and are in series then,
By rearranging the terms, then the above equation is written as,
By taking reciprocal on both sides of the above equation, then the above equation is written as,
By substituting the terms given terms in the above equation, then
On further simplification, then
On dividing, then the above equation is written as,
Now, the potential difference across three capacitors and (Here is the combined capacitance of and )
By substituting the charge and the capacitance in the above equation, then
On further simplification, then
On dividing the terms in the above equation, then
The sum of the charge of the capacitors and are,
(Here is the combined capacitance of and )
Now, substituting the combined capacitance of and , and the potential difference in the above equation, then
On multiplying, then
Thus, the above equation shows the sum of final charges and .
Hence, the option (A) is correct.
Note:- The capacitors and are in series, so the capacitor in series formula is used. Then, we have to find the total charge across the second capacitor and the third capacitor, so the equivalent capacitance of and are multiplied with the potential difference.
Formulae Used:
Capacitor in series,
Where,
Potential difference in capacitor,
Where,
Complete step-by-step solution:
Given that,
A capacitor,
Voltage
The capacitance is,
Capacitor in series, and the capacitors
By rearranging the terms, then the above equation is written as,
By taking reciprocal on both sides of the above equation, then the above equation is written as,
By substituting the terms given terms in the above equation, then
On further simplification, then
On dividing, then the above equation is written as,
Now, the potential difference across three capacitors
By substituting the charge and the capacitance in the above equation, then
On further simplification, then
On dividing the terms in the above equation, then
The sum of the charge of the capacitors
Now, substituting the combined capacitance of
On multiplying, then
Thus, the above equation shows the sum of final charges
Hence, the option (A) is correct.
Note:- The capacitors
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