Measuring the resistance of a block.

A rectangular conducting homogeneous (which means the material is the same throughout) block has dimensions 1 c m × 2 c m × 3 c m 1cm \times2 cm \times3 cm . A voltage V is applied between all opposite faces of the block and the corresponding currents were recorded. What is the maximum current measured in Amps if the minimum current recorded is 1 m A 1mA .


The answer is 0.009.

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1 solution

David Mattingly Staff
May 13, 2014

The resistance in a conductor is proportional to the length of the conductor and inversely proportional to its cross section. If we apply a voltage V to the 1 × 2 1\times2 face, the current will be given by I x y = V ρ x y z I_{xy}= \frac{V}{\rho} \frac{x y}{z} where x = 1 c m , y = 2 c m , z = 3 c m x=1 cm, y=2 cm, z=3 cm and ρ \rho is the resistivity of the material. By comparing the ratios x y z \frac{xy}{z} , x z y \frac{xz}{y} and y z x \frac{yz}{x} we find that I m a x I m i n = 9 I m a x = 9 mA . \frac{I_{max}}{I_{min}}= 9 \rightarrow I_{max}=9 \textrm{mA}.

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