A constant voltages is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

In the given circuit all resistances are of value $$R$$ $$ohm$$ each. The equivalent resistance between $$A$$ and $$B$$ is :

In a meter bridge, as shown in the figure, it is given that resistance $$Y = 12.5\,\,\Omega $$ and that the balance is obtained at a distance $$39.5$$ $$cm$$ from end $$A$$ (by Jockey J). After interchanging the resistances $$X$$ and $$Y$$, a new balance point is found at a distance $${l_2}$$ from end $$A.$$ What are the value of $$X$$ and $${l_2}$$ ?

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P₁ , P₂ and P₃ respectively, then :