How many bulbs need to be connected in series to give the same illumination as that produced by 10 bulbs in parallel. (All the bulbs are of the same type)
Assume the illumination produced by each bulb is dependent only on the power produced and each bulb can withstand any voltage across it or any current flowing through it.
Let the resistance of each bulb be R and the voltage of the electric source be V. When the 10 bulbs are connected in parallel, the power produced by each bulb is V^2/R. For 10 bulbs it is 10*V^2/R and as the illumination is dependent only the power it can be taken as 10*V^2/R
Now we have to find the number of bulbs that need to be connected in series to get the same illumination. If the number is N, the equivalent resistance of connecting N bulbs is N*R. The power produced when they are connected to the voltage source is V^2/(N*R)
To make 10*V^2/R equal to V^2/N*R, N would have to be equal to 1/10 which is not possible as you cannot have one tenth of a bulb.
It is not possible to use the same type of bulbs and connect them in series to produce the same illumination as that given by 10 of the bulbs connected in parallel.