In a metre-bridge when a resistance in the left gap is $2\  \Omega$ and unknown resistance in the right gap, the balance length is found to be $40\  \mathrm{~cm}$. On shunting the unknown resistance with $2\  \Omega$, the balance length changes by :

When two resistance $R_1$ and $R_2$ connected in series and introduced into the left gap of a meter bridge and a resistance of $10 \Omega$ is introduced into the right gap, a null point is found at $60 cm$ from left side. When $R_1$ and $R_2$ are connected in parallel and introduced into the left gap, a resistance of $3 \Omega$ is introduced into the right-gap to get null point at 40 cm from left end. The product of $R_1 R_2$ is $………….\Omega$

In the circuit shown $P \ne R$, the reading of the galvanometer is same with switch $S$ open or closed. Then

In the circuit shown in the adjoining figure, the current between $B$ and $D$ is zero, the unknown resistance is of ……………. $\Omega$

Resistance are connected in a meter bridge circuit as shown in the figure. The balancing length $l_{1}$ is $40\,cm$. Now an unknown resistance $x$ is connected in series with $P$ and new balancing length is found to be $80\,cm$ measured from the same end. Then the value of $x$ will be $…….\Omega$