Understanding Resistance for DC Motor Efficiency

When it comes to electrical engineering, understanding the fundamentals can feel like trying to decipher a puzzle. Take, for instance, our question: What resistance is required for a DC motor to operate at full speed with a current of 10 Amperes and a supply of 12 Volts? The options are diverse: 12 ohms, 120 ohms, 1.2 ohms, and 0.12 ohms. It's easy to trip up, but let’s break it down together.

Have you ever found yourself in a situation where knowledge of basic principles could save you time and effort? That's where Ohm's Law comes in. This remarkable law states that Voltage (V) is equal to the product of Current (I) and Resistance (R). It’s kind of like a friendship: if one person (the voltage) is feeling down (low), the other two (current and resistance) have to step up balance things out.

So how do we apply this law to our motor problem? In our case, the motor operates at a supply voltage of 12 Volts and draws a current of 10 Amperes. Let’s rearrange this equation to solve for resistance, shall we?

The formula we'll use is R = V / I. Substituting in our values gives us:

R = 12 V / 10 A = 1.2 ohms.

Voilà! The answer is 1.2 ohms. Now, why is this important? By ensuring that the resistance is exactly 1.2 ohms, our motor draws 10 Amperes from a 12 Volt supply, allowing it to function at full speed.

Isn't it fascinating how learning just one equation can enable you to understand the operational efficiency of devices that power our modern world? This principle applies not only to motors but also to various components within electrical systems, ensuring everything operates efficiently and safely.

For folks studying or working in electrical engineering, grasping these concepts is crucial. Equipment failures can be costly, not to mention the safety hazards involved. That’s why thorough calculations—like determining the resistance required for a DC motor—are more than just academic exercises; they’re foundational skills that can prevent real-world issues.

So, the next time someone asks you about DC motors or resistance, you'll not only have the answer, but you’ll also appreciate the practical significance of what was once just a number and formula on a page. It’s all about making those connections and understanding how every element plays its part in the grand design of electrical systems.