The correct answer is: C. balancer connected to lightly- loaded side runs as a motor.
In a D.C. 3-wire distributor using balancers and having unequal loads on the two sides, the balancer connected to the lightly-loaded side will run as a motor. This is because the current will flow from the heavily-loaded side to the lightly-loaded side, and the balancer will act as a motor to provide the necessary current.
The other options are incorrect. Option A is incorrect because both balancers cannot run as generators at the same time. This is because the current cannot flow in both directions at the same time. Option B is incorrect because both balancers cannot run as motors at the same time. This is because the current cannot flow in both directions at the same time. Option D is incorrect because the balancer connected to the heavily-loaded side will not run as a motor. This is because the current will flow from the lightly-loaded side to the heavily-loaded side, and the balancer will act as a generator to provide the necessary current.