Question

the table shows the values for current, i, in an electric circuit and the resistance, r, of the circuit. use the table to complete parts (a) through (c).
i (amperes) 1.5 3.0 4.5 6.0 7.5 9.0 12.0 15.0
r (ohms) 48.0 24.0 16.0 12.0 9.6 8.0 6.0 4.8
a. graph the ordered pairs in the table of values, with values of i along the x - axis and values of r along the y - axis. connect the eight points with a smooth curve. choose the correct gra
below.
b. does current vary directly or inversely as resistance? use your graph and explain how you arrived at your answer.
a. directly since the current values increase as resistance increases.
b. inversely since the current values increase as resistance increases.
c. inversely since the current values decrease as resistance increases.
d. directly since the current values decrease as resistance increases.
c. write an equation of variation for i and r, using one of the ordered pairs in the table to find the constant of variation. then use your variation equation to verify the other seven ordered
pairs in the table.
r =

Explanation:

Step1: Check the relationship between \(I\) and \(R\)

For inverse variation, \(I\times R = k\) (constant).
Take \(I = 1.5\), \(R=48\), then \(I\times R=1.5\times48 = 72\)
Take \(I = 3.0\), \(R = 24.0\), then \(I\times R=3.0\times24.0=72\)
Take \(I = 4.5\), \(R = 16.0\), then \(I\times R=4.5\times16.0 = 72\)
Since \(I\times R\) is constant (\(k = 72\)), the relationship is inverse variation.
The general equation for inverse variation is \(R=\frac{k}{I}\)

Step2: Write the equation of variation

Since \(k = 72\), the equation is \(R=\frac{72}{I}\)

Answer:

\(R=\frac{72}{I}\)