Question

Length of Rheostat (cm) Reading on the DMM (Ohms) 20 cm 30 cm 40 cm

To see if there is a linear relation between the length of the rheostat and the number of ohms, use Excel to draw a graph of reading on the DMM (Ohms) (on the y-axis) versus obstacle (on the ?-axis). Add a linear trend-line. Display the equation of the trend-line and the value of R²

What value of R² do you get for this graph and what is the significance of this number?

What can you conclude about the concept of obstacle and the physical quantity measured in ohms?

You may have come across the relation ? = ? (?/?) in your physics class. You have graphed the reading on the DMM (Ohms) versus obstacle (or length). This means that the slope of your graph was ?/A. The resistivity of Kanthal wire used in this lab is 1.45 x 10^-4 Ohm ∗ cm. The diameter of the 30 awg wire is 0.254 mm. Calculate the cross-sectional area, ?, of the wire (assuming that the wire is circular). Calculate the ratio ?/? and compare it with the slope of your graph. Do they agree?

Comment on how the slope of the graph can be used to convert ohms to cm of Kanthal.

Answer 1

Here is the plot between DMM and length

X . Y .. 5.3 8.4 11.1 LINEAR X-range: 20 - 40 y = mx + b m: 0.29 b: -0.4333 r: 0.9992 RMSE: 0.1633 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0

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slope =  $\rho$ / A = 0.29 ohm/ cm

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What can you conclude about the concept of obstacle and the physical quantity measured in ohms

Here, obstacle is nothing but a resistance. A rheostat is a device to set the resistance in a circuit. By varying the length, we are actually changing the length and thus changing the resistance and this will lead to change in reading for DMM

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R = $\rho$ L / A

R / L = $\rho$ / A

so,

$\rho$ / A = 1.45e-4 / pi * 0.0127² ( i have found radius from given diameter and converted to cm )

$\rho$ / A = 0.286 ohm /cm

so,

let's compare it with the value of  $\rho$ / A from slope

% error = 1.4 %

so,

yes we can say that value of slope and theoretical value agree with each other.