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A wire of length ' $r$ ' and resistance $100 \Omega$ is divided into $10$ equal parts. The first $5$ parts are connected in series while the next $5$ parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:
The number of electrons flowing per second in the filament of a $110 \mathrm{~W}$ bulb operating at $220 \mathrm{~V}$ is : (Given $\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$ )
Thirteen resistances each of resistance $R\, ohm$ are connected in the circuit as shown in the figure below. The effective resistance between $A$ and $B$ is
Two resistances ${R_1}$ and ${R_2}$ are made of different materials. The temperature coefficient of the material of ${R_1}$ is $\alpha $ and of the material of ${R_2}$ is $ - \beta $. The resistance of the series combination of ${R_1}$ and ${R_2}$ will not change with temperature, if ${R_1}/{R_2}$ equals
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.
When $5\ V$ potential difference is applied across a wire of length $0.1\ m$, the drift speed of electrons is $2.5 \times 10^{-4}$ $ms^{-1}$ . If the electron density in the wire is $8 \times 10^{28}$ $m^{-3}$ the resistivity of the material is close to