The figure is a part of a closed circuit. Find the currents i₁, i₂ and i₃

IMPORTANT RULE :- WHENEVER THERE ARE CURRENTS COMING FROM DIFFERENT WIRES AND GOING INTO SINGLE ANOTHER DIFFERENT WIRE (THROUGH WHICH THERE IS NO CURRENT COMING) THEN THE CURRENTS ARE ADDED AND IF CURRENT THROUGH ONE WIRE IS GOING INTO TWO DIFFERENT WIRES (WHICH DO NOT HAVE ANY CURRENT RUNNING THROUGH THEM INSTEAD OF THIS CURRENT) THEN THE CURRENT IS DIVIDED IN THEM ACCORDINGLY AND SUBTRACTED FROM THE MAIN COMING CURRENT.

If we know the main current one partition we can find other by using simple maths.

For example- 3A is the main current for forward going 1A and i₂ , and 1A and i₂ are the partitions of 3A current.

As there is law of conservation of energy.

There is always conservation of current(charge) ,

So 3 = 1 + i₂ , by which we can get i₂ which is = 3-1 = 2A.

Now to calculate i₁ we must obtain the equation of it , which is

i₁ + 2 = 3 , i₁ = 3-2 = 1A.

Now to calculate i₃ we will look at the point where it is getting divided and by whom that is , what is the main current of i₃ and the second partition of the main current which is companion with i₃,

As i₂ = 2A is the main current and it’s one partition is 1.5A and second partition is i₃ , so ,

i₂ = i₃ + 1.5 , 2 = i₃ + 1.5 , i₃ = 2 - 1.5 = 0.5A