The same mass of copper is drawn into two wires $1\, mm$ and $2\, mm$ thick. Two wires are connected in series and current is passed through them. Heat produced in the wire is in the ratio
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A heating coil can heat the water of a vessel from $20\,^oC$ to $60\,^oC$ in $30$ minutes. Two such heating coils are put in series and then used to heat the same amount of water through the same temperature range. The time taken now will be ............ $min$ (neglecting thermal capacity of the coils)
A wire of resistance $x$ ohm is drawn out, so that its length is increased to twice its original length, and its new resistance becomes $20 \,\Omega$, then $x$ will be ........ $\Omega$
$n$ identical cells are joined in series with two cells $A$ and $B$ with reversed polarities. $emf$ of each cell is $E$ and internal resistance is $r$. Potential difference across cell $A$ and $B$ is : $(n > 4)$
A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V _0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio $P_2: P_1$ is $\sqrt{x}: 1$. The value of $x$ is $.............$.
A current of $5\, A$ passes through a copper conductor (resistivity $= 1.7\times10^{-8}\,\Omega \,m$) of radius of cross-section $5\, mm$. Find the mobility of the charges if their drift velocity is $1.1\times10^{-3}\, m/s$ ................ $m^2/Vs$