In a meter bridge experiment, the balance point is obtained at length $l_1$ cm from the left end when resistances in the left gap and right gap are $15 \text{ } \Omega$ and $R \text{ } \Omega$ respectively. When the resistance $R$ is shunted with an equal resistance, the new balance point is at $1.6 l_1$. The resistance $R$ in ohm is:

Explain how the value of an unknown resistor can be obtained by using a meter bridge.

In a meter bridge experiment,the ratio of the left gap resistance to the right gap resistance is $2:3$. The balance length from the left end is (in $\,cm$)

$A$ resistance of $2 \Omega$ is connected across one gap of a metre-bridge (the length of the wire is $100 \text{ cm}$) and an unknown resistance,greater than $2 \Omega$,is connected across the other gap. When these resistances are interchanged,the balance point shifts by $20 \text{ cm}$. Neglecting any corrections,the unknown resistance is (in $\Omega$)

In an experiment to determine the temperature coefficient of resistance of a conductor,a coil of wire $X$ is immersed in a liquid. It is heated by an external agent. $A$ meter bridge setup is used to determine the resistance of the coil $X$ at different temperatures. The balancing points measured at temperatures $t_1=0^{\circ} C$ and $t_2=100^{\circ} C$ are $50 \ cm$ and $60 \ cm$ respectively. If the standard resistance taken out is $S=4 \ \Omega$ in both trials,the temperature coefficient of the coil is

In the circuit shown, a meter bridge is in its balanced state. The meter bridge wire has a resistance of $0.1 \, \Omega/cm$. The value of the unknown resistance $X$ and the current drawn from the battery of negligible internal resistance are: