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, Diffcult
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(c) ${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 ${V_{BC}} = 100 - {V_{AB}} = 75\,V$
$Q = C \times V = \frac{5}{2} \times 100 = 250\,\mu C$
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 ${V_{BC}} = 100 - {V_{AB}} = 75\,V$
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