Using Ohm's Law (V=IR), where units are volts, amperes, and ohms, and V is a constant 12, calculate:
a) The average rate of change of I with respect to R for the interval from R=8 to R=8.1
b) The rate of change of R with respect to I when I = 1.5
To calculate the average rate of change of I with respect to R, we need to find the change in I divided by the change in R for the given interval.
a) The average rate of change of I with respect to R for the interval from R=8 to R=8.1 can be calculated as follows:
Step 1: Substitute the given values into Ohm's Law: V = IR.
12 = I * 8 (at R = 8)
12 = I * 8.1 (at R = 8.1)
Step 2: Solve for I at R = 8:
12 = I * 8
I = 12/8
I = 1.5 amps
Step 3: Solve for I at R = 8.1:
12 = I * 8.1
I = 12/8.1
I ≈ 1.48 amps
Step 4: Calculate the change in I:
ΔI = I₂ - I₁
ΔI ≈ 1.48 - 1.5
ΔI ≈ -0.02 amps
Step 5: Calculate the change in R:
ΔR = R₂ - R₁
ΔR = 8.1 - 8
ΔR = 0.1
Step 6: Calculate the average rate of change of I with respect to R:
Average Rate of Change = ΔI / ΔR
Average Rate of Change ≈ -0.02 / 0.1
Average Rate of Change ≈ -0.2 amps per ohm
Therefore, the average rate of change of I with respect to R for the interval from R=8 to R=8.1 is approximately -0.2 amps per ohm.
b) To find the rate of change of R with respect to I when I = 1.5, we can rearrange the Ohm's Law equation to solve for R:
Step 1: Rearrange Ohm's Law equation: V = IR
R = V / I
Step 2: Substitute the given values:
R = 12 volts / 1.5 amps
R = 8 ohms
Step 3: Calculate the rate of change of R with respect to I:
Rate of Change = dR / dI
Rate of Change = 0 (since R is constant)
Therefore, the rate of change of R with respect to I when I = 1.5 is 0 ohms per amp.