Question

A square aluminium rod is 1 m long and 5 mm on edge. What must be the radius of another aluminium rod whose length is 1 m and which has the same resistance as the previous rod ?

• A. 5.0 mm
• B. 4.2 mm
• C. 2.8 mm
• D. 1.4 mm

Answer 1

Answer: (C)

2.8 mm

Let radius of another aluminium rod is $r^{\prime }$

Here $l=l^{\prime }=1m$

As both have same material so both have same resistivity i.e $\rho ={\rho }^{\prime }$

Here $R=R^{\prime }$

or $\frac{\rho l}{A}=\frac{{\rho }^{\prime }{l}^{\prime }}{A^{\prime }}$

or $A^{\prime }=A$

or $\pi r^{\prime 2}=5^2$

or $r^{\prime }=2.8mm$