Four resistances 40 $$\Omega $$, 60 $$\Omega $$, 90 $$\Omega $$ and 110 $$\Omega $$ make the arms of a quadrilateral ABCD. Across AC is a battery of emf 40 V and internal resistance negligible.The potential difference across BD in V is _______.

In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is $$l$$ = 25 cm. If R is replaced by a wire of half length and half diameter that of R of same material, then the balancing distance $$l'$$ (in cm) will now be________.

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 _____$$\Omega $$.