Question

How to find i1, i2,i3

Answer 1

to find i1, i2, and i3 we need to find the total current.

to find the total current, you need to find the total resistance

you're already given the total voltage, Vs

to find Rtotal, start from the resistors furthest from the voltage source.

R3 and R4 are in series so

Rtotal= R3+R4 = 6+3 = 9 ohms

9 ohms is now in parallel with R2 so,

Rtotal= $(\frac{1}{R3+R4}) ^{-1}$ + (\frac{1}{R2}) ^{-1})^-1= (1/18)^-1 +( 1/9)^-1 = 6 ohms

6 ohms is in series with R1 so

Rtotal=  4+6=10 ohms

itotal= (\frac{Vtotal}{Rtotal})

= 120 v/10 ohms = 12 A

i total = i1 because all the current flows through it

i1= 12A

so the current splits into i2 and i3 and the amount of current that flows through a branch depends on the total resistance in each branch.

we already calculated the resistance in the R3+R4 & R2 branch as 6 ohms

since r3 and r4 are in series, the same current will flow through them

r3+r4 = 9 ohms

r2= 18 ohms

so the current in r2 will be half that of R3 & R4 (V=IR)

using the current divider rule

$Ix = Itotal * \frac{Rtotal}{Rx}$

i2= 12A x (6 ohms/18 ohms)= 4 A

i3= 12A x (6 ohms/9 ohms) = 8 ohms