question_answer

In the figure below, what is the potential difference between the point A and B and between B and C respectively in steady state                                                                          [IIT 1979]

A)                                                      \[{{V}_{AB}}={{V}_{BC}}=100\,V\]

B)                                      \[{{V}_{AB}}=75\,V,\ {{V}_{BC}}=25\ V\]

C)                    \[{{V}_{AB}}=25\,V,\ {{V}_{BC}}=75\ V\]

D)            \[{{V}_{AB}}={{V}_{BC}}=50\ V\]

Correct Answer: C

Solution :

           \[{{C}_{eq}}=\frac{(3+3)\times (1+1)}{(3+3)+(1+1)}+1=\left( \frac{6\times 2}{6+2} \right)\,+1\]\[=\frac{5}{2}\mu F\] \ \[Q=C\times V=\frac{5}{2}\times 100=250\mu C\] Charge in \[6\mu F\] branch \[=VC=\left( \frac{6\times 2}{6+2} \right)\,100\]\[=150\,\mu C\] \[{{V}_{AB}}=\frac{150}{6}=25\,V\] and \[{{V}_{BC}}=100-{{V}_{AB}}=75\,V\]