According to Ohms Law the voltage V current I and resistance

According to Ohm\'s Law, the voltage V, current I, and resistance R in a circuit are related by the equation V = I R, where the units are volts, amperes, and ohms. Assume that voltage is constant with V = 12 volts. Calculate the average ROC of I with respect to R for the interval from R = 8 to R = 8.1 ohms. Calculate the ROC of I with respect to R when R = 8 ohms Calculate the ROC of R with respect to I when I = 1.7 amps.

Solution

a) V = IR = 12
If R = 8.0 = 12/8 = 1.5
If R = 8.1, I = 12/8.1 = 1.481481481...
So the average rate of change of I with respect to R is:
(12/8 - 12/8.1) / (8 - 8.1)
= 5/27 =~ 0.185185185...A/ohm

b) IR = 12, I = 12/R = 12R^-1
dI/dR = -12R^-2
When R = 8, dI/dR = -12(8)^-2 = -12/64 = -3/16 = -0.1875 A/ohm

c) IR = 12, R = 12/I = 12I^-1
dR/dI = -12I^-2
When I = 1.5, dI/dR = -12(1.5)^-2 = -16/3 = -5.333... ohm/A