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Charges on Conductors

Consider the ...

Question

Consider the circuit given below. After a long time,

The potential at junctions

A, B

are

8 V

and

2 V

respectively

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The potential at junctions

A, B

are

10 V

and

4 V

respectively

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The voltage across capacitance is

2 V

and charge stored in it is

2 μ C

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The voltage across capacitance is

6 V

and charge stored in it is

6 μ C

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Solution

The correct options are
A The potential at junctions $A, B$ are $8 V$ and $2 V$ respectively
D The voltage across capacitance is $6 V$ and charge stored in it is $6 μ C$
After a long time, capacitor is fully charged and no charge flows through it.
$V_{A} \to$ potential at left junction
$V_{B} \to$ potential at right junction
Current through left branch,
$I_{A} = \frac{10 V}{5 Ω} = 2 A$
$\Rightarrow V_{A} = 10 - 2 (1) = 8 V$
Current through right branch
$I_{B} = \frac{10 V}{10 Ω} = 1 A$
$\Rightarrow V_{B} = 10 - 8 (1) = 2 V$
$\Rightarrow V_{A} - V_{B} = (8 - 2) V = 6 V$

Charge stored in capacitor, $Q = C (V_{A} - V_{B}) = 6 μ C$

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