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when S2 is closed the "path of least resistance" will take up most of the current
so the current would flow through S2 rather than through B cause here B has resistance
for (i) we use power= VI
we don't have I so we replace I with V/R which we take from the equation R=V/I
power=v^2/r
R=38.4
ii) they are talking about total poser
so if S1 open there is no power you get this one right because the circuit is not complete
S1 and S2 closed as i said current always takes easier path so it will not go through B so in P=IV I=O the P is also 0 for B but then the current flows through A so its 1.5k+0=1.5k
if all of them are closed here again we will take power of B as 0 and if you see we have A and C in parallel Total power=P1+P2......... SO 1.5+1.5
S1 is closed so so we have A and B in series 1/total power = 1/p1 + 1/p2 +............
so 1/total power= 1/1.5 +1/1.5
total power =0.75
here s1 and S3 are closed so we have A and B parallel to C ie (AB) parallel to C for parallel Total power=P1+P2.........
and we already found AB which is 0.75 so now we just need to add 1.5
