CapacitanceHard

Question

The figure shows a diagonal symmetric arrangement of capacitors and a battery. If the potential of C is zero, then  (All the capacitors are initially uncharged).
                                                         

Options

A.VA = + 20 V
B.4(VA − VB) + 2(VD − VB) = 2VB
C.2(VA − VD) + 2(VB − VD) = 4VD
D.VA = VB + VD

Solution


given VC = 0 in AEFC VA  − 20 = VC    ⇒   VA = 20 V     Ans
by KCL, at point D
2 (VA − VD) + 2 (VB − VD) + 4 (VC − VD) = 0
2 (VA − VD) + 2 (VB − VD) =  4 VD                 ..... (i)         Ans
by KCL, at point B
4 (VA − VB) + 2 (VD − VB) + 2 (VC − VB) = 0
4 (VA − VB) + 2 (VB − VD) = 2VB                      ........(ii)    Ans
adding eq (i) and (ii)
2 (VA − VD) + 2 (VB − VD) + 4 (VA − VB) + 2 (VB − VD) = 4VD + 2 VB 
⇒    6VA = 6 VD + 6VB     ⇒    VA = VD + VB 

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