How to get the equation of graph 1 over V vs R

Mathematics

ScanSolve AI Answer

Answer

V=2RV = 2R

Step-by-step solution

5 steps
  1. Identify the type of graph.

    The graph shows Voltage (V) on the y-axis and Resistance (R) on the x-axis. It appears to be a straight line passing through the origin.

  2. Recall the equation for a straight line passing through the origin.

    This is given by y=mxy = mx, where mm is the slope.

  3. In this case, yy corresponds to Voltage (VV) and xx corresponds to Resistance (RR).

    So the equation becomes V=mRV = mR.

  4. Determine the slope (mm) of the line.

    The slope is calculated as the change in yy divided by the change in xx. From the graph, we can pick two points. Let's use the origin (0,0)(0,0) and another point, for example, (2 Ω,4 V)(2 \text{ } \Omega, 4 \text{ } V).
    The slope m=ΔVΔR=4 V−0 V2 Ω−0 Ω=4 V2 Ω=2 Ω−1m = \frac{\Delta V}{\Delta R} = \frac{4 \text{ } V - 0 \text{ } V}{2 \text{ } \Omega - 0 \text{ } \Omega} = \frac{4 \text{ } V}{2 \text{ } \Omega} = 2 \text{ } \Omega^{-1}.

  5. Substitute the slope back into the equation V=mRV = mR.

    V=(2 Ω−1)RV = (2 \text{ } \Omega^{-1})R.

    The equation of the graph is V=2RV = 2R.

    V=2RV = 2R

    V = 2R

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