All of the resistors in the circuits shown are identical as

All of the resistors in the circuits shown are identical, as are all of the batteries. Rank the current at the upper right-hand comer of each circuit Explain your reasoning.

Solution

Let I be current, V be EMF of battery, and R= resistance of single resistors.

Now if we neglect the resistance of wire, I will be (respectively for A to F):

V/2R , V/R , V/3R , V/R , V/2R , 2V/R

This gives following order in decreasing magnitude of I:

F>D=B>E=A>C

Now, if we assume that the resistivity of wire is not negligible then Resistannce of wire will be directly proportional to its length (R_wire=  l/A).

So correct order would be: F,B,D,E,A,C