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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The current in a conductor varies with time t as $I = 2t + 3{t^2}$ where $I$ is in ampere and $t$ in seconds. Electric charge flowing through a section of the conductor during $t = 2\,\sec$ to $t = 3\,\sec$ is ............. $C$
Water boils in an electric kettle in $20$ minutes after being switched on. Using the same main supply, the length of the heating element should be. . . . . . .to . . . . . .. times of its initial length if the water is to be boiled in $15$ minutes.
Two rods of copper and iron with the same cross-sectional area are joined at $S$ and a steady current $I$ flows through the rods as shown in the figure. Choose the most appropriate representation of charges accumulated near the junction $S$.
In an aluminium $(A1)$ bar of square cross section, a square hole is drilled and is filled with iron ( $Fe$ ) as shown in the figure. The electrical resistivities of $A 1$ and $Fe$ are $2.7 \times 10^{-8} \ \Omega m$ and $1.0 \times 10^{-7} \ \Omega m$, respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is
A $5\ V$ battery with internal resistance $2\,\Omega$ and a $2\,V$ battery with internal resistance ln are connected to a $10\,\Omega$ resistor as shown in the figure.
A potentiometer has uniform potential gradient. The specific resistance of the material of the potentiometer wire is $10^{-7} \, ohm-meter$ and the current passing through it is $0.1\, ampere$; cross-section of the wire is $10^{-6}\, m^2$. The potential gradient along the potentiometer wire is
A potentiometer wire has length $4\,\, m$ and resistance $8\,\,\Omega $. The resistance that must be connected in series with the wire and an accumulator of e.m.f. $2\,\, V,$ so as to get a potential gradient $1\,\, m \,V$ per $cm$ on the wire is ............. $\Omega$