In a potentiometer experiment two cells of $e.m.f.$ $E_1$ and $E_2$ are used in series and in conjunction and the balancing length is found to be $58\, cm$ of the wire. If the polarity of $E_2$ is reversed, then the balancing length becomes $29\, cm$. The ratio $\frac{{{E_1}}}{{{E_2}}}$ of the $e.m.f.$ of the two cells is
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Four lamps are connected in the way shown in the figure. When switch $S_2$ is open and switch $S_1$ is on position $-2$ , lamp $-b$ is the brightest, and lamp $-c$ and lamp $-d$ are the dimmest and are of the same brightness. Now $S_2$ is closed and $S_1$ is on position $-1$ , the sequence in brightness of the lamps is (with the first in the sequence being the brightest)
When a current of $2\, A$ flows in a battery from negative to positive terminal, the potential difference across it is $12\, V$. If a current of $3 \,A$ flows in the opposite direction potential difference across the terminals of the battery is $15\, V$, the $emf$ of the battery is ................ $\mathrm{V}$
In the circuit shown, the current through the $4\,\Omega $ resistor is $1\, amp$ when the points $P$ and $M$ are connected to a d.c. voltage source. The potential difference between the points $M$ and $N$ is ............... $volt$
In the circuit shown in figure, the power which is dissipated as heat in the $6\,\Omega $ resistor is $6\,W$. What is the value of resistance $R$ in the circuit? ................ $\Omega$