Problem 1-7: Circuit Reduction - Current Divider

Find $I_9$ (Hint: use circuit reduction).
All resistors are $10\Omega$ and $Is_1=10A$

Solution
Let's redraw the circuit:



The equivalent resistances are:$R_a= R_{10}+R_6+R_{11}+R_8+R_7=50 \Omega$

$R_b= R_a ||(R4+R_5)=50 || 20 = \frac{100}{7} \Omega$

$R_c= R_b+R_2+R_3=\frac{240}{7} \Omega$

Now, the circuit is reduced to:

Using current divider:

$I_9=\frac{R_c}{R_9+R_c} \times Is_1= 7.742 A$