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Ohm's Law is a fundamental principle used to understand electrical circuits. It explains the relationship between voltage, current, and resistance. The law is expressed with the formula:\[ V = I \times R \]where:

• \( V \) is the voltage across the circuit in volts (V),
• \( I \) is the current flowing through the circuit in amperes (A),
• \( R \) is the resistance of the circuit in ohms (\( \Omega \)).

When applied correctly, Ohm's Law can help you calculate any one of these values if the other two are known. In the context of a motor, Ohm’s Law is crucial because it helps identify the voltage drop across the motor's resistance and the impact of back EMF. Knowing how to manipulate the formula allows one to work out intricate details of electric circuits efficiently.

Motor resistance is the internal opposition to the flow of electric current within the motor. This resistance is mainly due to the armature winding within the motor and is a critical factor in calculating how the motor operates in different phases, such as startup and normal operation.
The resistance influences how much current flows and how much voltage is dropped across the motor itself when voltage is applied. In our example, the motor's resistance is stated as \( 0.720 \Omega \). Understanding this allows us to determine other important parameters like the back EMF or the initial surge of current when the motor is powered on. Motor resistance directly affects energy efficiency and heat generation inside the motor.

Starting current, also known as inrush current, is the initial surge of current that flows into the motor when it is first turned on. This surge occurs because the motor has not begun moving yet, and thus has not started generating back EMF that would otherwise reduce the voltage across the motor.
When a motor starts, the resistance to current flow is minimal, causing a high current draw. In the exercise example, the starting current is found to be \( 166.67 \mathrm{A} \) for a motor with a resistance of \( 0.720 \Omega \) and a supply voltage of \( 120.0 \mathrm{V} \). The starting current is typically much higher than the running current, potentially causing damage or unnecessary stress to the motor. Hence, asking how to limit this starting current without impacting the motor's performance becomes essential.

Series resistance involves adding a resistor in series with the motor circuit to limit the amount of starting current the motor receives. It's a crucial method because it reduces the initial current surge encountered at startup, thus protecting the motor from possible damage.
In our example, to limit the starting current to a safe \( 15.0 \mathrm{A} \), a series resistance of \( 7.28 \Omega \) is calculated. By using this additional resistance, you can ensure that the starting current does not exceed desired levels. The formula used for this calculation involves similar principles to Ohm’s Law:\[ V = I \times (R + R_s) \]where \( R_s \) is the series resistance required. This setup offers a practical solution to control the starting current, maintaining the motor's health and function.