Consider the circuit shown with identical identical meaning

Consider the circuit shown with identical (identical meaning the same resistance R) bulbs. Rank the 6 currents in order of greatest to least. Write a current in each blank, and indicate greater than (>), equal to (=), or less than (

Solution

Lets say that bulb has a resistance of R and the system is under a voltage of V with the connecting wires of negligible resistance:
A. Because of law of continuity it is maintained that I1 = I6, I2 = I4, I3 = I5. Also I1 = I2+I3 because of Kirchof\'s law. therefore for given V voltage
current I3 = V/R and I2 = V/(2R)
So, I1 = 16 > I3 = I5 > I2 = I4

B. I2 = 9 - 3 (Kirchof\'s law) = 6 A
and remaining, I6 = 9A, I5 = 3A, I4 = 6A

C. V1 = 15 Volt, Between V2 and V3 this is equally distributed therefore V2 = 7.5 and V3 = 7.5