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The figure given below shows a network of four capacitors of capacitance equal to C 1 = C , C 2 = 2 C , C 3 = 3 C , C 4 = 4 C are connected to a battery. If the ratio of charges on C 2 a n d C 4 is p q then what is the value of p + q , where p and q are smallest positive integers.

Correct answer

25

Step-by-step solution

The charge flowing through C 4 is q 4 = C 4 × V = 4 C V The series combination of C 1 , C 2 a n d C 3 1 C ′ = 1 C + 1 2 C + 1 3 C 1 C ′ = 6 + 3 + 2 6 C = 11 6 C ⇒ C ′ = 6 C 11 Now, C ′ a n d C 4 form parallel combination giving C " = C ′ + C 4 = 6 C 11 + 4 C = 50 C 11 Net Charge, q = C " V = 50 11 C V q ′ = q - q 4 = 50 11 C V - 4 C V = 6 C V 11 Total Charge flowing through C 1 , C 2 and C 3 will be q ′ = q - q 4 = 50 11 C V - 4 C V = 6 C V 11 Since, C 1 , C 2 , C 3 are in series combination. Hence, charge flowing

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