The resistance of a coil is $4.2\, \Omega$ at $100\,^o C$ and the temperature coefficient of resistance of its material is $ 0.004\,^o C$. Its resistance at $0\,^o C$ is ............. $\Omega$
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Figure shows a thick shell made of electrical conductivity $\sigma$ and has inner & outer radii of $10\ cm$ & $20\ cm$ respectively and is filled with ice inside it. Its inside and outside surface are kept at different potentials by a battery of internal resistance $\frac{2}{\pi} \Omega \ \&\ \in = 5V$. Find value of $\sigma$ for which ice melts at maximum possible rate if $25\%$ of heat generated by shell due to joule heating is used to melt ice.
A $2\, W$ carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is .............. $mA$
The current in a wire varies with time according to relation $I = 4 + 2t$. The quantity of charge which has passed through a crosssectionn of the wire during the time $t = 2\, s$ to $t = 6\, s$ will be .............. $\mathrm{C}$