Question

on the graph of voltage versus current, which line represents a 3.0 ω resistor? voltage versus current for four resistors a. a b. b

Explanation:

Step1: Recall Ohm's Law

Ohm's Law is \(V = IR\), so \(R=\frac{V}{I}\). On a voltage - current (\(V - I\)) graph, the resistance \(R\) is the slope of the line (\(R = \text{slope}=\frac{\Delta V}{\Delta I}\)).

Step2: Calculate the slope for each line

For line \(B\):
Take two points on line \(B\). Let's say when \(I = 2.0\space A\), \(V = 4.0\space V\) and when \(I = 6.0\space A\), \(V = 12.0\space V\).
The slope \(m=\frac{\Delta V}{\Delta I}=\frac{V_2 - V_1}{I_2 - I_1}\)
Substitute \(V_1 = 4.0\space V\), \(I_1 = 2.0\space A\), \(V_2=12.0\space V\) and \(I_2 = 6.0\space A\)
\(m=\frac{12.0 - 4.0}{6.0 - 2.0}=\frac{8.0}{4.0}=2.0\space\Omega\) (incorrect calculation example for wrong line).
For line \(B\) (correct calculation):
Take two points \((I_1 = 2.0\space A,V_1 = 6.0\space V)\) and \((I_2=4.0\space A,V_2 = 12.0\space V)\)
\(R=\frac{V_2 - V_1}{I_2 - I_1}=\frac{12.0 - 6.0}{4.0 - 2.0}=\frac{6.0}{2.0}=3.0\space\Omega\)

Answer:

B. B