How is it possible to do this?
The total electric current in the wire leading to a group of 2 resistors in parallel connection is given by the formula: IT = (V/R1) + (V/R2) where IT = total electrical current, V = potential difference, and R1 and R2 are two resistances.
IT = 420/3x
V = 120
R1 = 15
R2 = 2x - 4
Find the values of IT.
The smaller value of IT is ____
The larger value of IT is ____
2007-11-03 10:57:17 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
IT = (V/R1) + (V/R2)
420/3x = 120/15 + 120/(2x-4)
140/x = 8 + 60/(x-2)
divide by 4
35/x = 2 + 15/(x-2)
multiply x(x-2)
35(x-2) = 2x(x-2) + 15x
expand
35x - 70 = 2x^2 - 4x + 15x
2x^2 - 24x + 70 = 0
divide by 2
x^2 - 12x + 35 = 0
(x-5)(x-7) = 0
so x=5 or x=7
if x=5, IT = 420/3x = 140/x = 140/5 = 28
if x=7, IT = 420/3x = 140/7 = 20
therefore
The smaller value of IT is 20.
The larger value of IT is 28.
2007-11-03 11:15:54 · answer #1 · answered by zsm28 5 · 1⤊ 0⤋
You plug the values given into the equation for IT and cross-multiply to eliminate x in the denominator. This gives you a quadratic equation which you can solve for x, and then for IT. Being a quadratic, it will have two solutions.
2007-11-03 11:10:38 · answer #2 · answered by injanier 7 · 0⤊ 0⤋