The series combination of two batteries, both of the same emf 10 V, but different internal resistance of 20$$\Omega $$ and 5$$\Omega $$, is connected to the parallel combination of two resistors 30$$\Omega $$ and R $$\Omega $$. The voltage difference across the battery of internal resistance 20$$\Omega $$ is zero, the value of R (in $$\Omega $$) is : _______

Four resistances of 15$$\Omega $$, 12$$\Omega $$, 4$$\Omega $$ and 10$$\Omega $$ respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10$$\Omega $$ to balance the network is _____$$\Omega $$.

The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of 10 $$\Omega $$ is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the ceil is $${N \over {10}}$$ $$\Omega $$ , where N is an integer then value of N is .............