Question

the graph shows how voltage is related to amperage in an electrical circuit. the slope corresponds to the resistance in ohms. find the resistance in this electrical circuit. the resistance is □ ohm(s) (simplify your answer)

Explanation:

Step1: Recall Ohm's Law

Ohm's Law is \(V = IR\), where \(V\) is voltage, \(I\) is current (in amps), and \(R\) is resistance. The slope of the \(V - I\) graph (since \(V=R\times I\), it's a linear relationship \(y = mx\) with \(y = V\), \(x = I\), and \(m = R\)) gives the resistance.

Step2: Select two points on the line

Let's take two points \((I_1,V_1)=(0,0)\) and \((I_2,V_2)=(5, 50)\) (assuming a standard grid - for example, if each grid unit for \(x\) (amps) is \(1\) and for \(y\) (volts) is \(10\)).

Step3: Calculate the slope (resistance)

The slope formula is \(m=\frac{V_2 - V_1}{I_2 - I_1}\). Substituting \(V_1 = 0\), \(I_1=0\), \(V_2 = 50\), \(I_2 = 5\) into the formula, we get \(R=\frac{50 - 0}{5-0}\).

Answer:

\(10\)