Figure shows a part of an electric circuit.The potentials at the points a,b and c are 30V,12V and 2V

Figure shows a part of an electric circuit.The potentials at the points a,b and c are 30V,12V and 2V respectively.Find the currents through the three resistors

Let potential at the point o XV.

(30−x)=10ii.

(x−12)=20i2

(x−2)=30i3

i1=i2+i3

⇒30−x10=x−1220+x−230

⇒30−x=x−122+x−23

⇒30−x=3x−36+36+2x−46

⇒180−6x=5x−40

⇒11x=220

⇒x=22011=20V

ii=30−2010=1A

i2=20−1220=0.4A

i3=20−230=610=0.6A