Question

What length of German silver wire, diameter 0.050cm, is needed to make a 28 resistor, if the resistivity of German silver is $2.2 \times {10^{ - 7}}\;{\rm{m}}$?
A. 20
B. 25
C. 30
D. 35

Answer 1

In this question, we are going to use the relation between the resistance, length of the wire, diameter of the wire and the resistivity of the wire. Based up on the given values we can easily calculate the length of the wire.

Complete Step by Step Answer:
The diameter of the silver wire is
$\begin{array}{l} d = 0.05\;{\rm{cm}}\\\ r = 0.00025\,{\rm{m}} \end{array}$
The resistivity of German silver is$\rho = 2.2 \times {10^{ - 7}}\;{\rm{m}}$.
The resistance of the wire is $R = 28\;\Omega$.
The equation of the resistance,
$R = \rho \dfrac{I}{A}$
Here, l is the length of the german silver wire.
Substitute the values in the above equation.
$\begin{array}{l} R = \rho \dfrac{I}{A}\\\ 28 = 2.2 \times {10^{ - 7}} \times \dfrac{l}{{\pi \times {{0.00025}^2}}}\\\ l = \dfrac{{28 \times 3.14 \times {{0.00025}^2}}}{{2.2 \times {{10}^{ - 7}}}}\\\ = \dfrac{{0.0000055}}{{0.00000022}}\\\ = 24.9 \approx 25\,{\rm{m}} \end{array}$
Therefore, the option is (b), the correct answer is 25 m.

Note: Be sure that the area of the wire is taken as in terms of radius, then convert the diameter into radius and check the length of the wire whether it is in cm or m.