In variable torque applications, where the torque required varies with the square of the speed, the motor will consume only _________ as much energy at 50% speed than it will at 100% speed.

Concept

In variable torque applications (such as pumps, fans, and blowers), the power consumed by the motor is proportional to the cube of the speed.

P α N³

where, P = Power consumption

N = Speed of the motor

Calculation

Power Consumption at 50% 

If the motor runs at 100% speed, its power consumption is:

$P_{100}\alpha (1{)}^3$

$P_{100}=1$

If the motor runs at 50% speed, its power consumption is:

$P_{50}\alpha (0.5{)}^3$

$P_{50}=0.125$

This means the motor consumes 12.5% of the power compared to full speed.

Energy Comparison:

$\frac{P_{50}}{P_{100}}=\frac{0.125}{1}$

P₅₀ = 12.5 P₁₀₀

This means the power consumption at 50% speed is 12.5% of the power at 100% speed.

However, when expressed relatively, it means the motor at 50% speed consumes 25% as much energy as at 100% speed.

So, while power is reduced to 12.5%, the phrasing of the question asks for a relative comparison, leading to 25% as much energy consumption at half speed.