Find the charge and potential difference across C1 of capacitance 1 µF for the given circuit?

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AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 2)
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  1. 2/3 µC, 4/3 V
  2. 4/3 µC, 4/3 V
  3. 2/3 µC, 2/3 V
  4. 3/4 µC, 3/4 V

Answer (Detailed Solution Below)

Option 2 : 4/3 µC, 4/3 V
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Detailed Solution

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Concept:

Calculating the equivalence capacitance, from the left side.

We can see that C1 and C4 are in parallel 

therefore

Ce1 = C1 + C4      ....(1)

Now this equivalence will be in series with C2 capacitor

      ...(2)

Calculation:

By equation 1,

⇒ Ce1 = 1 + 1

By equation 2,

⇒ Ce2 = 2/3μF 

Thus, the total charge flowing through the circuit

⇒ Q = 2/3 μF × 4V

⇒ Q = 8/3μC

Charge across will the capacitance will be in the ratio of respective capacitance 

CeqV = C1V + C2V + C3V

Q1 = Q/2

⇒ Q1 = 4/3 μC

Now potential difference across C1 can be calculated as

⇒ V1 = 4/3V

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