Question

A rod of a certain metal is $1.0\, m$ long and $0.6\, cm$ in diameter. Its resistance is $3.0 \times 10^3\, \Omega$ Another disc made of the same metal is $2.0\, cm$ in diameter and $1.0\, mm$ thick. What is the resistance between the round faces of the disc?

• A. $1.35 \times 10^{-8} \, \Omega$
• B. $2.70\times 10^{-7} \, \Omega$
• C. $4.05 \times 10^{-6} \, \Omega$
• D. $8.10 \times 10^{-5} \, \Omega$

Answer 1

Answer: (B)

$2.70\times 10^{-7} \, \Omega$

Answer 2

As, $R=\rho l / A=\rho l /\left(\pi d^{2} / 4\right)$ Resistance for a given material is directly proportional to the length and inversely proportional to the square of diameter of round faces. So for the second rod, diameter is $2.0 / 0.6=10 / 3$ times diameter of the first one. and, length is $1.0 \,mm / 1 \,m =1 / 1000$ times the length of first one. Thus resistance of the second rod is, $\frac{1 / 1000}{(10 / 3)^{2}}=9 \times 10^{-5}$ times the resistance of the first one. So resistance of the second rod is $3 \times 10^{-3} \times 9 \times 10^{-5}=2.70 \times 10^{-7} \,\Omega$