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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 :

155464_97d665f5664d4ff89e2c6598a510f7cb.png

A
VA=+15V
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B
4(VAVB)+2(VDVB)=2VB
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C
4(VAVD)+2(VBVD)=4VD
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D
VA=VB+VD
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Solution

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

VAVB<VAVDVB>VD

Now if 2μF is connected between B and D, charge will flow from B to D and finally VB>VD.

VA=20V.

At junction B:

q2=q1+q3

or (VAVB)4=(VBVD)2+(VBVC)2

or 4(VAVB)+2(VDVB)=2VB

At junction D:

q2=q1+q3

or 4(VDVC)+2(VAVD)+2(VBVD)

or 2(VAVD)+2(VBVD)=4VD

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