when devices are connected in series, what is common in them, current or voltage?
because in a derivation of power, in series combination of devices, voltage is taken as common... Derivation is as follows
P1, P2, P3 is power at voltage V, with resistances R1, R2, R3.
R=R1+R2+R3; R/V=R1/Vsq + R2/Vsq + R3/Vsq;

1/P= 1/P1 + 1/P2 + 1/P3;
can you please explain why and how voltage is common in them because in some of the questions when connected in series, current was taken as common.
In case if any one of them can be taken common as per the question, can you explain when!!

R/V=R1/Vsq + R2/Vsq + R3/Vsq

1/P= 1/P1 + 1/P2 + 1/P3

This is incorrect for resistors is series. For resistors in series the current is common, and also sum of all the voltage drops across all resistors equals the total voltage drop. Thus for a series circuit of three resistors:

R= R1 + R2 + R3
V= V1 + V2 + V3 = iR1 + iR2 + iR3 = I(R1 + R2 +R3) = iR

From this you can see that V/R = I, and I = V1/R1 = V2/R2 = V3/R3.

As for power: P = I^2R = I^2(R1 + R2 + R3) = P1 + P2 + P3.