In order to determine the $e.m.f.$ of a storage battery it was connected in series with a standard cell in a certain circuit and a current $I_1$ was obtained. When the battery is connected to the same circuit opposite to the standard cell a current $I_2$ flow in the external circuit from the positive pole of the storage battery was obtained. What is the $e.m.f$. $\varepsilon_1$ of the storage battery? The $e.m.f$. of the standard cell is $\varepsilon_2$.
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Water boils in an electric kettle in $15\,\min$ after switching on. If the length of the heating wire is decreased to $2/3$ of its initial value, then the same amount of water will boil with the same supply voltage in ............. $min$
$A \,6 \,V$ battery of negligible internal resistance is connected across a uniform wire of length $1\, m$. The positive terminal of another battery of emf $4\,V$ and internal resistance $1\, \Omega$ is joined to the point $A$ as shown in figure. The ammeter shows zero deflection when the jockey touches the wire at the point $C$. The $AC$ is equal to
A wire of length $5\,m$ and radius $1\,mm$ has a resistance of $1\, ohm$. What length of the wire of the same material at the same temperature and of radius $2\,mm$ will also have a resistance of $1\, ohm$ .............. $m$
A potentiometer wire is $100\,\, cm$ long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at $50\,\, cm$ and $10\,\, cm$ from the positive end of the wire in the two cases. The ratio of emf's is
A car battery of $e.m.f$. $12\,V$ and internal resistance $5 \times {10^{ - 2}}\,\Omega $, receives a current of $60\; A$ from external source, then terminal voltage of battery is
Two batteries of $e.m.f.$ $4\,V$ and $8 \,V$ with internal resistances $1\, \Omega$ and $2\,\Omega$ are connected in a circuit with a resistance of $9 \,\Omega$ as shown in figure. The current and potential difference between the points $P$ and $Q$ are
In a Wheatstone bridge (see figure) Resistance $P$ and $Q$ are approximately equal. When $R = 400\,\Omega ,$ the bridge is balanced. On interchanging $P$ and $Q,$ the value of $R,$ for balance is $405\,\Omega .$ The value of $X$ is close to ................. $ohm$
The resistance of a wire is $R$. It is bent at the middle by $180^{\circ}$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is