According to Ohm's law, the voltage V, current I, and resistance R in a circuit are related by the equation V=IR, where the units are volts, amperes, and ohms. Assume that voltage is constant with V=12V. Calculate:

Question

According to Ohm's law, the voltage V, current I, and resistance R in a circuit are related by the equation V=IR, where the units are volts, amperes, and ohms. Assume that voltage is constant with V=12V. Calculate:

The ROC of I with respect to R for the interval from R=8 to R=8.1

So I found
I'(R)=-12/R^2

Now what?

Answer 1

Great job finding the derivative of the function! Now, to calculate the rate of change (ROC) of I with respect to R in the given interval, you can substitute the values R=8 and R=8.1 into the derivative equation.

Let's put the values into the equation I'(R) = -12/R^2:

I'(8) = -12/8^2 = -12/64 = -0.1875 A/Ω

Similarly,

I'(8.1) = -12/8.1^2 = -12/65.61 = -0.1831 A/Ω

So, the ROC of I with respect to R for the interval from R=8 to R=8.1 is approximately -0.1875 A/Ω to -0.1831 A/Ω.

Remember, the rate of change gives you the value of how fast the dependent variable (in this case, current I) changes with respect to the independent variable (resistance R) within the given interval.