Figure shows a situation similar to the previous problem. All parameters are the same except that a battery of emf ϵ and a variable resistance R are connected between O and C. Neglect the resistance of the connecting wires. Let θ be the angle made by the rod from the horizontal position (shown in the figure), measured in the clockwise direction. During the part of the motion 0 < θ < π/4 the only forces acting on the rod are gravity and the forces exerted by the magnetic field and the pivot. However, during the part of the motion, the resistance R is varied in such a way that the rod continues to rotate with a constant angular velocity ω. Find the value of R in terms of the given quantities.
Given:
Emf = ϵ
Resistance = r
Angle made by rod = θ
Angular velocity = w
Formula used:
From the previous questions, induced emf 
… (i), where B = magnetic field, w = angular velocity, a = radius
Hence, Total emf = 
Total current i = total emf/resistance = 
… (ii), where R = resistance
‘Now, net force on the rod 
… (iii),
where mgcosθ = component of weight along rod, where m = mass, g = acceleration due to gravity, θ = angle made by rod with horizontal, and ilB = Magnetic force, where i = current, l = length of rod, B= magnetic field.
Since the rod rotates with uniform angular velocity, net torque about O = 0.
Hence, torque = net force x distance from line of action = 
, where a = radius of rod
Therefore, 
… (iii)
Hence, 
⇒ 
(Ans)