State Kirchhoff’s first law and the physical quantity that is conserved according to this law.

The S.I. base units for resistance ($\Omega$) are ${kg\; m}^2{s}^{-3}{A}^{-2}$. Use the equation for electrical conductivity:

to determine the S.I. base units for conductivity $\sigma$.

A student investigates the electrical properties of a uniform wire using a circuit in which the length $L$ of the wire connected in series with a cell of e.m.f. $E$ and internal resistance $r$ is varied. The student plots a graph of $\frac{1}{I}$ on the vertical axis against the connected wire length $L$ on the horizontal axis, where $I$ is the current.

Show that the relationship between $\frac{1}{I}$ and $L$ is given by:

where $\rho$ is the resistivity of the wire and $A$ is its cross-sectional area.

In this experiment, the cell has an e.m.f. of $2.0V$ and the uniform wire has a diameter of $0.45mm$. The straight line of best fit on the student’s graph has a gradient of $3.20A^{-1}{m}^{-1}$. Determine the resistivity $\rho$ of the material of the wire.

The student later realizes that they made a systematic error because the contact at the start of the wire was shifted, meaning all measured values of $L$ are shorter than the actual values by a constant length. Explain why this systematic error does not affect the value of the resistivity calculated in (ii).