Question

None of the resistors in the circuit shown in the drawing is connected in series or in parallel with one another. (Let I1 = 8.6 A, I2 = 6.2 A, and I3 = 12.2 A.)

(a) Find the current I₅.
(b) Find the resistance R₂.
(c) Find the resistance R₃.

Answer 1

this can be done by Kirchhoff's voltage rule
first applying it in left top square
moving anticlockwise
I₁*4+I₂*R₂= 75

8.6*4+6.2*R₂=75

R₂=6.55 ohm

current in R₄by Kirchhoff's current rule

I₄=I₁-I₂

= 8.6-6.2

=2.4 A

now applying it in left lower loop

I₄R₄+I₅R₅=I₂R₂

2.4*2+2.2 I₅ =6.2*6.55

I₅=7.40 A

now applying it in right loop

I₃R₃+I₅R₅=75

12.2*R3+7.40*2.2=75

R₃₌ 4.81 ohm