A current of 6 A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 2 Ω each and leaves by the corner R. The currents i1 in ampere is ______. 

CONCEPT:

Kirchoff's law is having two types which are written as;

1. Kirchoff's current law - Kirchoff's current law is defined as the total current entering a junction being equal to the charge leaving the junction.
2. Kirchoff's voltage law - Kirchoff's voltage law is defined as states that the voltage around a loop equal to the sum of every voltage drop in the same loop for any closed network is equal to zero.

CALCULATIONS:

According to Kirchoff's law, at point P the current is written as;

I₁ + I₂ = 6     ----(1)

Again Kirchoff's law of voltage, the closed circuit equation is written as;

-2I₁ - 2I₁ +2I₂ = 0

⇒ -4I₁ + 2I₂ = 0

⇒ 2I₁ - I₂ = 0     ----(2)

Now, by adding equations (1) and (2) we have;

I1 + I2 + 2I1 - I2 = 6

⇒ 3I₁ = 6

⇒ I₁ = 2 A

Now, by putting the equation (2) we have;

\(2\times 2 \) - I₂ = 0

⇒ 4 - I₂ = 0

⇒ I₂ = 4 A

Hence, the current in I₁ is 2 A.