Two cells when connected in series are balanced on $8\;m$ on a potentiometer. If the cells are connected with polarities of one of the cell is reversed, they balance on $2\,m$. The ratio of $e.m.f.$'s of the two cells is
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The current in a simple series circuit is $5.0\, amp$. When an additional resistance of $2.0\, ohms$ is inserted, the current drops to $4.0\, amp$. The original resistance of the circuit in $ohms$ was
A potentiometer having the potential gradient of $2\, mV/cm$ is used to measure the difference of potential across a resistance of $10 \,\Omega$. If a length of $50\, cm$ of the potentiometer wire is required to get the null point, the current passing through the $10 \,\Omega$ resistor is (in $mA$)
When the current $i$ is flowing through a conductor, the drift velocity is $v$. If $2i$ current is flowed through the same metal but having double the area of cross-section, then the drift velocity will be
For the arrangement of the potentiometer shown in the figure, the balance point is obtained at $a$ distance $75\,cm $ from $A$ when the key $k$ is open. The second balance point is obtained at $60\, cm$ from $A$ when the key $k$ is closed. Find the internal resistance (in $ \Omega$) of the battery $E_1$.
Current density in a cylindrical wire of radius $R$ is given as $J =$ $\left\{ {\begin{array}{*{20}{c}}
{{J_0}\left( {\frac{x}{R} - 1} \right)\,\,for\,\,0 \leqslant x < \frac{R}{2}} \\
{{J_0}\frac{x}{R}\,\,\,\,for\,\,\,\frac{R}{2} \leqslant x \leqslant R}
\end{array}} \right.$The current flowing in the wire is: