The effective resistance of two resistors in parallel is $\frac{{12}}{7}\,\Omega $. If one of the resistors is disconnected the resistance becomes $4$ $\Omega$. The resistance of the other resistor is.............. $\Omega$
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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
In the figure the potentiometer wire of length $l =100\, cm$ and resistance $9\Omega$ is joined to a cell of emf $E_1 = 10V$ and internal resistance $r_1 = 1\Omega $. Another cell of emf $E_2 = 5\, V$ and internal resistance $r_2 = 2 \Omega $ is connected as shown. The galvanometer $G$ will show no deflection when the length $AC$ is ............... $cm$
Two bulbs of $500\, watt$ and $200\, watt$ are manufactured to operate on $220\, volt$ line. The ratio of heat produced in $500\, W$ and $200\, W$, in two cases, when firstly they are joined in parallel and secondly in series, will be
A wire of resistance $R$ and radius $r$ is stretched till its radius became $r / 2$. If new resistance of the stretched wire is $x R$, then value of $x$ is $\qquad$
In the given circuit ' $a$ ' is an arbitrary constant. The value of $m$ for which the equivalent circuit resistance is minimum, will be $\sqrt{\frac{ x }{2}}$. The value of $x$ is ...........