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Factors Affecting Resistance & How They Affect

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Question

The figure shows a diagonal symmetric arrangement of capacitors and a battery. If the potential of $C$ is zero, then identify the incorrect statement :

V_{A} = + 15 V

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4 (V_{A} - V_{B}) + 2 (V_{D} - V_{B}) = 2 V_{B}

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4 (V_{A} - V_{D}) + 2 (V_{B} - V_{D}) = 4 V_{D}

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V_{A} = V_{B} + V_{D}

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Solution

The correct option is A $V_{A} = + 15 V$
If $2 μ F$ were not present between Band D, then potential drop across upper $4 μ F$ will be less than potential drop across lower $2 μ F$ i.e.,

$V_{A} - V_{B} < V_{A} - V_{D} \Rightarrow V_{B} > V_{D}$

Now if $2 μ F$ is connected between B and D, charge will flow from B to D and finally $V_{B} > V_{D}$ .

$V_{A} = 20 V$ .

At junction B:

$q_{2} = q_{1} + q_{3}$

or ${(V}_{A} - V_{B}) 4 = (V_{B} - V_{D}) 2 + (V_{B} - V_{C}) 2$

or $4 {(V}_{A} - V_{B}) + 2 (V_{D} - V_{B}) = 2 V_{B}$

At junction D:

$q_{2} = q_{1} + q_{3}$

or $4 {(V}_{D} - V_{C}) + 2 (V_{A} - V_{D}) + 2 (V_{B} - V_{D})$

or $2 {(V}_{A} - V_{D}) + 2 {(V}_{B} - V_{D}) = 4 V_{D}$

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The figure shows a diagonal symmetric arrangement of capacitors and a battery. If the potential of C is zero, then identify the incorrect statement :

The figure shows a diagonal symmetric arrangement of capacitors and a battery. If the potential of $C$ is zero, then identify the incorrect statement :