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Two resistances ${R_1}$ and ${R_2}$ are joined as shown in the figure to two batteries of $e.m.f.$ ${E_1}$ and ${E_2}$. If ${E_2}$ is short-circuited, the current through ${R_1}$ is
$12$ cells each having the same emf are connected in series and are kept in a closed box. Some of the cells are wrongly connected. This battery is connected in series with an ammeter and two cells identical with each other and also identical with the previous cells. The current is $3\, A$ when the external cells aid this battery and is $2\,A$ when the cells oppose the battery. How many cells in the battery are wrongly connected :-
A resistance of $2 \Omega$ is comnected across one gap of a metre-bridge (the length of the wire is $100 \mathrm{~cm}$ ) and an unknown resistance, greater than $2 \Omega$, is connected across the other gap. When these resistance are interchanged, the balance point shifts by $20 \mathrm{~cm}$. Neglecting any corrections, the unknown resistance 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 $1.1\times10^{-3}\, m/s$ ................ $m^2/Vs$