# Calculate the current on the resistor 5Ω using the method of source transformations!? Relevance

Step-1:

Replace the left 10V source and 5Ω resistance to a current source

I₁ = V₁/R₁ = 10V/5Ω = 2A

Similarly, replace the right 10V source and 15Ω resistance to a current source

I₂ = V₂/R₂ = 10V/15Ω = ⅔A

On left you will have current source I₁ with direction upwards and 5Ω resistance in parallel

On right you will have current source I₂ with direction to left and 15Ω resistance in parallel

Step-2:

Since we need current through middle resistor, we keep it untouched.

Add the 2 current sources and add find equivalent resistance of the 2 parallel resistances R₁and R₂

1/R₃ = 1/R₁ + 1/R₂ = 1/5Ω + 1/15Ω = 4/15

R₃ = 15/4 Ω

I₃ = I₁ + I₂ = 2A + ⅔A = 8/3 A

So we get a current source with direction upwards and resistance is parallel of 15/4 Ω

Step-3

Convert the current source to voltage source

V₃ = I₃R₃ = (8/3 A)(15/4 Ω) = 10 V

So we get a voltage source of 10V with positive up and a series resistance of 15/4 Ω, which is i series with the middle 5 Ω resistance

Step-4

Then we can find the the current through the 5Ω resistance by

I = V/R = (10V)(5Ω + 15/4 Ω) = 10/(35/4) = 8/7 A

• Calculate the current on the resistor 5Ω using the method of source transformations! • I' = 10/(5+75/20)*15/20 = 6/7 of Amps

I'' = 10/(15+5/2)/2 = 2/7 of Amps

I = I'+I'' = 6/7 + 2/7 = 8/7 of  A mps

Vxa = 5*8/7 = 40/7 of  Volts