What is the current drawn by a 3 horsepower, 100 V DC motor that is 85% efficient?

To determine the current drawn by a 3 horsepower DC motor operating at 100 V with an efficiency of 85%, we start by converting horsepower to watts since electrical formulas typically use watts for power. One horsepower is equivalent to approximately 746 watts. Therefore, a 3 horsepower motor can be calculated as follows:

3 HP * 746 W/HP = 2238 watts.

Next, we need to account for the efficiency of the motor. Since the motor is 85% efficient, the actual power input (the electrical power drawn from the source) must account for this efficiency. The input power can be calculated with the following relationship:

Input Power = Output Power / Efficiency.

Plugging in the values, we calculate the input power:

Input Power = 2238 W / 0.85 = 2639.41 watts.

Now, to find the current (I) drawn by the motor, we can use the formula that relates power (P), voltage (V), and current (I):

P = V * I.

Rearranging the formula gives us:

I = P / V.

Substituting the input power and the voltage:

I = 2639.41 W / 100 V = 26.394