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In an electrical cable there is a single wire of radius $9\, mm$ of copper. Its resistance is $5\,\Omega $. The cable is replaced by $6$ different insulated copper wires, the radius of each wire is $3\,mm$. Now the total resistance of the cable will be ............... $\Omega$
A metal wire of specific resistance $64 \times {10^{ - 6}}\,ohm - cm$ and length $198\, cm$ has a resistance of $7\, ohm$, the radius of the wire will be ............. $cm$
$A$ wire of cross-section area $A$, length $L_1$, resistivity $\rho_1$ and temperature coefficient of resistivity $\alpha_1$ is connected to a second wire of length $L_2$, resistivity $\rho_2$ , temperature coefficient of resistivity $\alpha_1$ and the same area $A$, so that wire carries same current. Total resistance $R$ is independent of temperature for small temperature change if (Thermal expansion effect is negligible)
A potentiometer wire has length $10\, m$ and resistance $20\,\Omega $. A $2. 5\, V$ battery of negligible internal resistance is connected across the wire with an $80\,\Omega $ series resistance. The potential gradient on the wire will be
A torch bulb rated as $4.5\, W$, $1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ................ $V$