To know the resistance G of a galvanometer by half deflection method, a battery of emf V_E and resistance R is used to deflect the galvanometer by angle $$\theta $$. If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F = − kv, where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)

In the circuit shown, the resistance r is a variable resistance. If for r = fR, the heat generation in r is maximum then the value of f is :

A series LR circuit is connected to a voltage source with
V(t) = V₀ sin$$\Omega $$t. After very large time, current I(t) behaves as
(t₀ >> $${L \over R}$$) :