Find the resistance of a heating coil that draws 4.8 A when the voltage across it is \(120 \mathrm{V}.\)

In the realm of electronics, electrical resistance is a measure of the opposition to the flow of electric current. Imagine trying to push water through a narrow pipe versus a wide one. The narrow pipe offers more resistance to the water flow, akin to how electrical resistance works. Various materials have different levels of resistance, which is why some materials are conductors (low resistance), like copper, and others are insulators (high resistance), such as rubber.

When dealing with resistance, it's key to bear in mind that its value determines how much current will flow for a given voltage. The higher the resistance, the lower the current flow, assuming the voltage is kept constant. This is particularly important to remember when troubleshooting circuits or designing electronic systems.

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The correlation between voltage and current in an electrical circuit is closely defined by Ohm's law. This fundamental principle in electronics states that the current through a conductor between two points is directly proportional to the voltage across the two points. In other words, if you increase the voltage across a fixed resistance, the current will rise proportionately and vice versa.

Expressing this relationship mathematically, the law is articulated as the formula: \( I = \frac{V}{R} \). Here, \( I \) represents the current in amperes, \( V \) is the voltage in volts, and \( R \) signifies the resistance in ohms (Ω). This equation is vital for anyone learning about electrical circuits, since manipulating it reveals how different changes in voltage and resistance will influence the current flowing through a circuit.

To find the resistance of an electrical component, Ohm's law provides a straightforward formula: \( R = \frac{V}{I} \). By rearranging the aforementioned relationship \( I = \frac{V}{R} \), you get this formula. To apply this formula, you need to know the voltage across the component and the current passing through it.

To illustrate this with a practical example, consider a heating coil drawing 4.8 A of current with a voltage of 120 V across it. Using the formula, the resistance \( R \) is \( \frac{120 \text{ V}}{4.8 \text{ A}} \), which equals 25 ohms. This method of calculating resistance is essential for designing circuits, determining the right components for an application, or even just to check if a component meets the specifications for a particular task.