In a potentiometer experiment, the galvanometer shows no deflection when a cell is connected across $60\, cm$ of the potentiometer wire. If the cell is shunted by a resistance of $6\,\Omega $, the balance is obtained across $50\, cm$ of the wire. The internal resistance of the cell is .............. $\Omega $
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$32$ cells, each of $emf$ $3V$, are connected in series and kept in a box. Externally, the combination shows an $emf$ of $84\, V$. The number of cells reversed in the combination is
A heating coil can heat the water of a vessel from $20\,^oC$ to $60\,^oC$ in $30$ minutes. Two such heating coils are put in series and then used to heat the same amount of water through the same temperature range. The time taken now will be ............ $min$ (neglecting thermal capacity of the coils)
The resistances of the four arms $P, Q, R$ and $S$ in a Wheatstone's bridge are $10\,ohm$, $30\,ohm$, $30\,ohm$ and $90\,ohm$, respectively. The e.m.f. and internal resistance of the cell are $7\,volt$ and $5\,ohm$ respectively. If the galvanometer resistance is $50\,ohm$, the current drawn from the cell will be ............... $A$
The temperature coefficient of resistance of tungsten is $4.5 \times 10^{-3}{ }^{\circ} C ^{-1}$ and that of germanium is $-5 \times 10^{-2}{ }^{\circ} C ^{-1}$. A tungsten wire of resistance $100 \,\Omega$ is connected in series with a germanium wire of resistance $R$. The value of $R$ for which the resistance of combination does not change with temperature is .......... $\Omega$
A steady current $I$ flows through a wire of radius $r$, length $L$ and resistivity $\rho$. The current produces heat in the wire. The rate of heat loss in a wire is proportional to its surface area. The steady temperature of the wire is independent of