Shown 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.

Explanation

Let potential at the point be x V
` Then (30-x) = 10i_1`
` (x-12) = 20i_2`
` (x-2) = 30i_3`
`Since i_1 = i_2 + i_3 `
` rArr ((30-x)/10) = ((x-12)/20) + ((x-2)/30)`
` rArr (30 -x) = ((x-12)/2) + ((x-2)/3) `
` rArr 30- x = (3x - 36 + 2x -4 /6)`
` rArr 180 - 6x = 5x - 40 `
` rArr 11x = 220 `
` rArr x = 220/11 = 20V.`
` i_1 = ((30-20)/10) = 1A`
` i_2 = ((20 - 12)/20) = 8/20 A `
=0.4 A
` i_3 = ((20-2)/30) A = 18/30A `
`= 6/10 A = 0.6A `.