## Powering a Motor

In the below circuit diagram, we are powering a brushless motor with a 20V battery. The resistance across the motor when running without a load is 50 ohms.

- How much current, in mA, will flow through the motor?
- What is the power, in watts, dissipated by the motor?
- If the motor ran for 15 minutes under the above conditions, what is the minimum battery capacity in mAh?

##
__
__**Hint**

**Hint**

Ohm's law:

$$$V=IR$$$

where
$$V$$
is the voltage,
$$I$$
is the current, and
$$R$$
is the resistance.

##
__
__**Hint 2**

**Hint 2**

Power absorbed by a resistive element:

$$$P=VI$$$

where
$$P$$
is power,
$$V$$
is the voltage, and
$$I$$
is the current.

To solve for the current, use Ohm's law:

$$$V=IR$$$

where
$$V$$
is the voltage,
$$I$$
is the current, and
$$R$$
is the resistance.

$$$I=\frac{V}{R}=\frac{20V}{50\Omega}=0.4A=400mA$$$

Power absorbed by a resistive element:

$$$P=VI$$$

where
$$P$$
is power,
$$V$$
is the voltage, and
$$I$$
is the current.

Solving for power dissipated by the motor:

$$$P=20V (0.4A)=8W$$$

To solve for capacity:

$$$400mA \times 15min \times \frac{1h}{60min}=100mAh$$$

- 400 mA
- 8 W
- 100 mAh