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Four wires of equal length and of resistances $10$ $ ohms$ each are connected in the form of a square. The equivalent resistance between two opposite corners of the square is ............. $ohm$
$A$ wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised by $\Delta T$ in time $t. N$ number of similar cells is now connected in series with a wire of the same material and cross section but of length $2L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. The value of $N$ is :
In a meter bridge experiment the balance point in obtained if the gaps are closed by $2\,\Omega$ and $3\,\Omega$. A shunt of $x\,\Omega$ is added to $3\,\Omega$ resistor to shift the balancing point by $22.5\,cm$. The value of $X$ is $................$