In the given figure, battery $E $ is balanced on $55\, cm$ length of potentiometer wire but when a resistance of $10 \,\Omega$ is connected in parallel with the battery then it balances on $50\, cm$ length of the potentiometer wire then internal resistance $r$ of the battery is ............. $\Omega $
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Four wires $AB,\,\,BC,\,\,CD,\,\,DA$ of resistance $4\, \Omega$ each and a fifth wire $BD$ of resistance $8\, \Omega$ are joined to form a rectangle $ABCD$ of which $BD$ is a diagonal. The effective resistance between the points $A$ and $B$ is
A potentiometer wire of length $L$ and a resistance $r$ are connected in series with a battery of e.m.f. $E_0$ and a resistance $r_1$. An unknown e.m.f. $E$ is balanced at a length $l$ of the potentiometer wire. The e.m.f. $E$ will be given by
A set of $n$ equal resistors, of value $R$ each, are connected in series to a battery of emf $E$ and internal resistance $R.$ The current drawn is $I.$ Now, the $n$ resistors are connected in parallel to the same battery. Then the current drawn from battery becomes $10\,I.$ The value of $n$ is
Three resistors each of $4\,\Omega $ are connected together to form a network. The equivalent resistance of the network cannot be ............ $\Omega$