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In an experiment to measure the internal resistance of a cell by potentiometer, it is found that the balance point is at a length of $2\,m$ when the cell is shunted by a $5\,\Omega $ resistance; and is at a length of $3\,m$ when the cell is shunted by a $10\,\Omega $ resistance. The internal resistance of the cell is, then ................ $\Omega $
A potentiometer wire has length $4\,\, m$ and resistance $8\,\,\Omega $. The resistance that must be connected in series with the wire and an accumulator of e.m.f. $2\,\, V,$ so as to get a potential gradient $1\,\, m \,V$ per $cm$ on the wire is ............. $\Omega$
The resistances in the two arms of the meter bridge are $5 \,\Omega$ and $R \,\Omega$ respectively. When the resistance $R$ is shunted with an equal resistance, the new balance point is at $1.6\,l_1$. The resistance $R$ is .................. $\Omega$
In the circuit diagram shown in figure given below, the current flowing through resistance $3\, \Omega$ is $\frac{ x }{3}\,A$. The value of $x$ is $...........$
A $220 \; V , 50 \; Hz$ AC source is connected to a $25 \; V$, $5 \; W$ lamp and an additional resistance $R$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $R$ (in ohm) will be