The resistances in the two gaps of a balanced meter bridge are 'X' $\Omega$ and '3X' $\Omega$ respectively. If the resistances are interchanged the balance point shifts by

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

In a potentiometer circuit when two cells of e.m.f. $1.5$ volt and $1.2$ volt are connected to assist each other, balancing length is $270$ cm. What will be the balancing length in cm when these two cells are connected in opposition?