Conductivity
Consider a 50 Ω resistor has a cross-sectional area of 0.125 m^2 and length of 100 mm. What is the material’s conductivity (S/m) inside the resistor?
Expand Hint
Conductivity is a property that determines a material’s ability to transmit or conduct an electric current. It is the reciprocal of resistivity.
$$$\rho=\frac{1}{\sigma}$$$
where
$$\rho$$
is resistivity and
$$\sigma$$
is conductivity.
Hint 2
A material’s resistivity within a resistor:
$$$\rho = \frac{RA}{L}$$$
where
$$R$$
is the resistor’s resistance,
$$A$$
is the resistor’s cross-sectional area, and
$$L$$
is the resistor’s length.
Resistivity is the material property that determines the resistance of a resistor, or how strongly it resists an electric current. A material’s resistivity within a resistor:
$$$\rho = \frac{RA}{L}$$$
where
$$R$$
is the resistor’s resistance,
$$A$$
is the resistor’s cross-sectional area, and
$$L$$
is the resistor’s length.
$$$\rho = \frac{(50\Omega)(0.125m^2)}{0.1m}=\frac{6.25\Omega\cdot m}{0.1}=62.5\:\Omega\cdot m$$$
Conductivity is a property that determines a material’s ability to transmit or conduct an electric current. It is the reciprocal of resistivity.
$$$\rho=\frac{1}{\sigma}$$$
where
$$\rho$$
is resistivity and
$$\sigma$$
is conductivity.
Solving for conductivity:
$$$\sigma=\frac{1}{\rho}=\frac{1}{62.5\:\Omega\cdot m}=0.016\:S/m$$$
0.016 S/m
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