evaluate currents in the circuitsdetermine

Question

Evaluate currents in the circuits:

Determine currents I₁ and I₂ in the given circuits by applying KVL.

Solution

We apply KVL for first loop :

10 = 1 I₁  + 1 ( I₁  - I ₂ )

10 = 2 I₁  - I ₂ ---------- (i)

KVL for second loop :

1 ( I ₂  - I₁ ) + 4 I ₂  = 0

5 I ₂  - I₁  = 0                   --------- (ii)

∴          I₂  =   I₁ /5 = 0.2 I₁                  --------- (iii)

Put the value of I₂ in Eq. (i)

10 = 2 I₁  - 0.2 I₁  = 1.8 I₁

⇒         I₁  = 5.55 Amp

From Eq. (iii), I₂  = 1.11 Amp .