Question

 A rectangular copper strip is 20 cm long, 0.1 cm wide and 0.4 cm thick. Determine the resistance between (i) opposite ends (ii) opposite sides. The resistivity of copper is 1.7 × 10–6 Ω cm​

Answer 1

Given,

The length of the strip$\[ = 20\]$

The breadth of the strip$\[ = 0.1\]$

The thickness of the strip$\[ = 0.4\]$

The resistivity of the copper$\[ = 1.7 \times {10^{ - 6}}\]$

Solution,

Formula used,$\[R = \frac{{\rho l}}{A}\]$

(i) Calculate the resistance between the opposite ends.

Therefore,

$\[\begin{array}{l} \Rightarrow R = \frac{{\left( {1.7 \times {{10}^{ - 6}}} \right) \times \left( {20} \right)}}{{\left( {0.1 \times 0.4} \right)}}\\ \Rightarrow R = 8.4 \times {10^{ - 6}}\Omega \end{array}\]$

(ii)Calculate the resistance between the opposite sides.

$\[\begin{array}{l} \Rightarrow R = \frac{{\left( {1.7 \times {{10}^{ - 6}}} \right) \times \left( {0.1} \right)}}{{\left( {20 \times 0.4} \right)}}\\ \Rightarrow R = 0.021 \times {10^{ - 6}}\Omega \end{array}\]$

Hence, the resistance between the opposite ends and opposite sides are $\[8.4 \times {10^{ - 6}}\Omega \]$ and $\[0.021 \times {10^{ - 6}}\Omega \]$ respectively.