What is the Rate of Change in Ohm's Law?

[sydneyfranke]

Homework Statement

According to Ohm's law, the voltage V, current I, and resistance R in a current are related by the equation V = IR, where the units are . . . Assume the voltage is constant V = 12V. Calculate:
a) The average ROC of I with respect to R for the interval from R = 8 to R = 8.1
b) The ROC of I with respect to R when R = 8
c) The ROC of R with respect to I when I = 1.5

Homework Equations

I'm assuming something like f(x) = lim(h->0) of f(x+h) - f(x)/h or finding the f'(x

The Attempt at a Solution

I'm not really even sure how to set this problem up. I have about a million problems with this homework set, have seen the teacher, have seen a tutor, nothing really seems to help.

 

[sydneyfranke]

If someone could at least send me a link of a similar problem so I can look at it, I would appreciate it.

 

[Mark44]

Homework Statement

According to Ohm's law, the voltage V, current I, and resistance R in a current are related by the equation V = IR, where the units are . . . Assume the voltage is constant V = 12V.

This means that IR = 12, or I = 12/R. So here I = I(R) is a function of R.

Calculate:
a) The average ROC of I with respect to R for the interval from R = 8 to R = 8.1

For the average rate of change, calculate (I(8.1) - I(8))/(8.1 - 8)

b) The ROC of I with respect to R when R = 8

Here you want the instantaneous rate of change -- dI/dR, evaluated at R = 8.

c) The ROC of R with respect to I when I = 1.5

Solve for R as a function of I, then take the derivative. Here you want the instantaneous rate of change -- dR/dI, evaluated at I = 1.5.

Homework Equations

I'm assuming something like f(x) = lim(h->0) of f(x+h) - f(x)/h or finding the f'(x

The Attempt at a Solution

I'm not really even sure how to set this problem up. I have about a million problems with this homework set, have seen the teacher, have seen a tutor, nothing really seems to help.