To find the current that a DC motor "draws" when operating at full load (full power output), we can use the power equation for DC circuits. The formula that relates power, voltage, and current is given by:
[tex]\[ P = V \times I \][/tex]
Where:
- [tex]\( P \)[/tex] is the power (in watts, W)
- [tex]\( V \)[/tex] is the voltage (in volts, V)
- [tex]\( I \)[/tex] is the current (in amperes, A)
Here are the steps to solve for the current:
1. Identify the given values:
- Power ([tex]\( P \)[/tex]) is given as 1.50 kilowatts (kW)
- Operating voltage ([tex]\( V \)[/tex]) is given as 300 volts (V)
2. Convert the power from kilowatts to watts:
[tex]\[ 1.50 \, \text{kW} = 1.50 \times 1000 \, \text{W} = 1500 \, \text{W} \][/tex]
3. Rearrange the power equation to solve for current ([tex]\( I \)[/tex]):
[tex]\[ I = \frac{P}{V} \][/tex]
4. Substitute the known values into the equation:
[tex]\[ I = \frac{1500 \, \text{W}}{300 \, \text{V}} \][/tex]
5. Perform the division to find the current:
[tex]\[ I = \frac{1500}{300} \, \text{A} = 5 \, \text{A} \][/tex]
So, the current drawn by the motor when operating at full load (full power output) is [tex]\( 5 \)[/tex] amperes (A).
