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Question
Three identical capacitors C1, C2 and C3 of capacitance 6 μF each are connected to a 12 V battery as shown.
Find
(i) charge on each capacitor
(ii) equivalent capacitance of the network
(iii) energy stored in the network of capacitors
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Solution
The 12 V battery is in parallel with C1, C2, and C3. C1 and C2are in series with each other while C3 is in parallel with the combination formed by C1and C2.
Total voltage drop across C3 = 12 V
q3 = CV
Where, q = Charge on the capacitor
C1, C2, C3 = 6 μF (Given in the question)
q3 = 6 × 12 = 72 μC
Voltage drop across C1 and C2 combined will be 12 V.
Let the voltage drop at C1 = V1
Let the voltage drop at C2 = V2
Then,
V = V1 + V2
`V_1 = q_1/C`
`V_2 = q_2/C`
`q_1/6+q_2/6 = 12`
As both the capacitors are in series,
`q_1 =q_2 =q`
Then,
`q{1/6 +1/6} =12`
`q xx 1/3 =12`
Or,
q = 36 micro coulombs
Thus, charge on each of C1 and C2 is 36 coulombs.
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