In the circuit below find the current through each resistor

In the circuit below, find the current through each resistor. E = 20v R_1 = 40 ohm R_2 = 80 ohm R_3 = 50 ohm

Solution

R2 and R3 are in series.

So, resultant of these two is R = R2+R3

                                            = 80 + 50 = 130 ohm

R and R1 are in parallel.

Let the resultant resistance be R \' then

(1/R \') = (1/R) +(1/R1)

         = (1/130)+(1/40)

         = (40 +130)/(40x130)

From this R \' = (40x130)/(40+130)

                   = 30.588 ohm

Emf E = 20 volt

Current in the circuit i = E/R \'

                                = 20 / 30.588

                                = 0.6538 A

Current through R1 is i1 = i[R/(R+R1)]

                                   = 0.6538 [130/(130+40)]

                                   = 0.6538(130/170)

                                   = 0.5 A

Current through R is i2 = i - i1

                                  = 0.6538A-0.5A

                                  = 0.1538 A

Current through R2 is = 0.1538 A

Current through R3 is = 0.1538 A