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Two cells, having the same $e.m.f.$ are connected in series through an external resistance $R.$ Cells have internal resistances $r_1$ and $r_2\,\, (r_1 > r_2)$ respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of $R$ is
The potential difference across the $100\,\Omega$ resistance in the following circuit is measured by a voltmeter of $900 \,\Omega$ resistance. The percentage error made in reading the potential difference is
In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance $P\, = 4\,\Omega $ and the neutral point $N$ is at $60\,cm$ from $A$. Now an unknown resistance $R$ is connected in series to $P$ and the new position of the neutral point is at $80\,cm$ from $A$ . The value of unknown resistance $R$ is
Three resistances, each of $1\, ohm$, are joined in parallel. Three such combinations are put in series, then the resultant resistance will be ............. $ohm$
Masses of three wires of copper are in the ratio of $1 : 3 : 5$ and their lengths are in the ratio of $5:3:1.$ The ratio of their electrical resistances are