Question

The voltage V across a semiconductor in a computer is given by Upper V equals alpha Upper I plus beta Upper I squared​, where I is the current​ (in A). If a 12​-V battery is conducted across the​ semiconductor, find the current if alphaequals5 Upper Omega and betaequals0.5 Upper Omega​/A.

Answer 1

The current that can flow in the semiconductor are 5 A and -12 A

Explanation:

The parameters are;

V = α·I + β·I²

I = Current (A)

When V = 12-V, α = 5 Ω, β = 0.5 Ω/A

We have;

12 = 5·I + 0.5·I²

Which gives, 24 = 10·I + I²

Moving all the terms to the right we have;

I² + 10·I - 24 = 0

By completing the square we have

(I + 5)² -25 - 24 = 0

(I + 5)² - 49 = 0

(I + 5)² = 49

I + 5 = ±7

I = 7 - 5 = 2 A or I = -7 - 5 = -12 A

Therefore the current values are = 5 A and -12 A

The semiconductor current values are 5 A and -12 A.