Electrical resistivity is a property of materials that quantifies how strongly they resist the flow of electric current. It is defined as the resistance of a material per unit length and cross-sectional area. The formula for resistivity (\( \rho \)) is given by:
Formula for Electrical Resistivity
The resistivity can be expressed mathematically as:
\( \rho = R \cdot \frac{A}{L} \)
Where:
- R = Resistance in ohms (Ω)
- A = Cross-sectional area in square meters (m²)
- L = Length in meters (m)
SI Unit of Electrical Resistivity
The SI unit of electrical resistivity is ohm-meter (Ω·m). This unit reflects the resistance of a material when it is 1 meter long and has a cross-sectional area of 1 square meter.
Effect of Doubling the Length of the Wire
In a series circuit, if the length of the wire is doubled, the resistance of the wire also doubles, assuming the cross-sectional area and material remain constant. According to Ohm's Law, which states:
\( V = I \cdot R \)
Where:
- V = Voltage
- I = Current
- R = Resistance
If the resistance increases due to the increased length, and the voltage remains constant, the current will decrease. Specifically, if the original current was 100 mA (0.1 A), doubling the resistance will halve the current, resulting in:
New Current = 0.1 A / 2 = 0.05 A (or 50 mA)
Justification
This change occurs because the increased resistance impedes the flow of electrons, leading to a reduction in current. Therefore, in this scenario, doubling the length of the wire results in a decrease in current through the circuit.
