3B Scientific Resistance Apparatus - Manual (Page 2)

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4.1 Resistance as a function of cross-
sectional area
• Connect the LCR meter to the sockets of the
Constantan wire with the smallest diameter
(refer to fig. 1).
• Measure its resistance R and fill it in a table.
• Calculate the cross sectional area A of the
wire by using the equation
⎟
⎠
⎞
⎜
⎝
⎛
⋅ π =
2
d
A
• Be sure to convert the diameter d into me-
ters before substituting.
• Repeat the procedure with the other Con-
stantan wires.
• Plot the graph of the resitance vs. cross
sectional area (refer to fig. 2).
Fig. 1 Experimental set-up
Fig. 2 Resistance as a function of the cross sectional
area
4.2 Calculating the resistivity
ρ of a wire
The equation for resistance R of a wire is given
by
A
L
R
⋅ ρ =
with L = length of the wire, A = cross sectional
area of the wire and
ρ = resistivity of the material
Solving our equation of resistance for ρ, we get:
L
A
R
⋅ = ρ
• Set up the experiment according to fig. 1.
• Connect the LCR to any of the constantan
wires and determine its resistance.
• Calculate the resistivity of Constantan.
• Repeat the experiment with the brass wire
and compare the resistivity of Constantan
and Brass.