Interpreting an XY Scatter Graph

Example Ohm’s Law

Data

If we set up a circuit with some resistor and an ammeter (to measure current) in series. And supply voltages 1,2,3,4, and 5 volts respectively, the currents (in milliAmperes) shown were measured.

Highlight the data, make an XY Scatter chart and choose Layout #9.

Label axes (including units), eliminate legend, change title.

Current versus Voltage

• In our set up, we controlled voltage. Furthermore we used the convention that the variable we controlled is plotted on the x-axis.

• Now we want to compare the fit line (Trendline) from Excel with the equation from our theory – Ohm’s Law. Excel: y = 0.2807x + 0.0019Theory V=IR

Rearranging

Identification (Part 1)

Identification (Part 2)

Right click on the Trendline, choose Format Trendline, check Set intercept

Identification (Part3)

Units of slope

• Slope is “rise over run” so its units are mA/V. • The resistance was the reciprocal of slope, so

its units are V/mA. • The m means milli means 10-3.• A factor of 10-3 in the denominator

corresponds to a factor of 10+3 in the numerator. 10+3 goes with kilo or k.

• A volt/ampere is an ohm. Thus we have units for the resistance in kilo-ohms.

Interpolation

• Our equation y = 0.2812x or I = 0.2812V allows us to guess what the current would be for voltages that we did not measure.

• For instance, we would expect the current corresponding to a voltage of 2.5 to be 0.2812*2.5 = 0.703 mA.

• When we use the Trendline to estimate a new value within our range (here 1-5 volts), this is called Interpolation.

Extrapolation

• We can also use our results to estimate what the current would be for voltages outside the range we measured.

• For instance, we would expect the current corresponding to a voltage of 6 to be 0.2812*6 = 1.6872 mA.

• When we use the Trendline to estimate a new value outside our range (here 1-5 volts), this is called Extrapolation.