What is the condition in which the heat produced in an electric circuit is :

(a) directly proportional

(b) inversely proportional

to the resistance of the circuit?

Compute the ratio of the total quantity of heat produced in the two cases.

The average drift speed of conduction electrons in a copper wire of cross-sectional area $3.0\times {10}^{-7} {\mathrm{m}}^2$ carrying a current of $5 \mathrm{A}$ is $x\times {10}^{-4} \mathrm{m} {\mathrm{s}}^{-1}$. Assume that each copper atom contributes roughly one conduction electron. The density of copper is $9.0\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and its atomic mass is $63.5 \mathrm{u}$. Write the value of $x$ to the nearest integer.

(Take $1 e=1.6\times {10}^{-19} \mathrm{C}$ and $N_A=6\times {10}^{23} {\mathrm{mol}}^{-1}$)