How can we find the equivalent of the two 10 ohm and one 30 ohm resistor? From the solution it looks like it's an 8.

Also can some one explain what's happening in 10(5) (10/50) part of the second equation ?

 

It is the right 10 plus the 30 in parallel with the left 10 which gives 8 ohms.

For the last part of the second equation, it uses the equation of a current divider made of two resistors in parallel (the left 10 and the right 10+30).

 

Can you re-explain the second part, I don't see it.

If its current divider shouldn't it be (last part only):

I= Req/R I
= 8/40 x 5 ?

 

I through the right 10=10(left)*5/[10(left)+(10(right)+30)]

 

how is that current divider ? it looks nothing like I= Req/R I

 

Just in case the sequence is not clear

1. The source sees a total resistance of 4Ω + 10Ω||40Ω + 8Ω = 20Ω

2. The current i(o) must be i(o) = 100/20 = 5A.

3. The current i(o) divides at the node where the 10Ω resistors meet

4. At this node current to the left I_10_LH = 5 x 40/50 [= 4A]

5. At this node current to the right I_10_RH = 5 x 10/50 [= 1A]

6. The voltage drop across the right hand 10Ω

V_10_RH = 10 x I_10_RH = 10 x 5 x 10/50 = 10V

 

I agree with all the points except 4 and 5.

I through the right resistor:
current divider : I= Req/R Isrc

Req= 10 left resistor// (10right resistor +30) = 8 ohm
R= (10 right resistor +30) = 40 ohm
Isrc= 5 A

 

I agree with all the points except 4 and 5.

I through the right resistor:
current divider : I= Req/R Isrc

Req= 10 left resistor// (10right resistor +30) = 8 ohm
R= (10 right resistor +30) = 40 ohm
Isrc= 5 A

Tnk uses another formula for calculating the current through two parallel resistors.

Your formula is for a general case with more than two parallel resistors. If you make the calculations you will get the same results.