How does the resistivity of alloys compare with those of pure metals from which they may have been formed?

$A$ battery is a source of maintaining a constant potential difference across two ends of a conductor.

Two bulbs $A$ and $B$ are rated as $90 \, W - 120 \, V$ and $60 \, W - 120 \, V$ respectively. They are connected in parallel across a $120 \, V$ source. Find the current in each bulb. Which bulb will consume more energy?

The electrical resistivity of a few materials is given below in ohm-metre. Which of these materials can be used for making the element of a heating device?

$A$. $6.84 \times 10^{-8} \, \Omega m$

$B$. $1.60 \times 10^{-8} \, \Omega m$

$C$. $1.00 \times 10^{-4} \, \Omega m$

$D$. $2.50 \times 10^{12} \, \Omega m$

$E$. $4.40 \times 10^{-5} \, \Omega m$

$F$. $2.30 \times 10^{17} \, \Omega m$

State the formula correlating the electric current flowing in a conductor and the voltage applied across it. Also, show this relationship by drawing a graph. What would be the resistance of a conductor, if the current flowing through it is $0.35 \ A$ when the potential difference across it is $1.4 \ V$?

$(a)$ Derive the formula for the calculation of work done when current flows through a resistor.
$(b)$ One electric bulb is rated $40 \ W$ and $240 \ V$ and another is $25 \ W$ and $240 \ V$. Which bulb has higher resistance and how many times?