Ohm's Law Calculations

1. From Analogy to Law

In the last lesson, we mentioned that current faces opposition. In our water analogy, this is like the narrowness of a pipe restricting water flow. An electrical component designed specifically to provide this opposition is called a resistor. Its property of opposition is called resistance, measured in Ohms ($\Omega$).

To start, let's solidify the intuition behind the relationship between voltage, current, and resistance.

The key takeaway from this analogy is that for a given pipe width (resistance), increasing the pressure (voltage) will increase the flow (current). This simple, direct relationship was first quantified by Georg Simon Ohm.

2. Ohm's Law: The Core Relationship

Ohm's Law states that the voltage across a resistor is directly proportional to the current flowing through it. The constant of proportionality is the resistance.

This is expressed in the famous equation:

$V=I\times R$

Where:

• $V$ is the voltage across the resistor (in Volts).
• $I$ is the current flowing through the resistor (in Amperes).
• $R$ is the resistance of the resistor (in Ohms).

This simple linear equation is the cornerstone of circuit analysis. It's the first tool you will reach for when examining a circuit. A component that follows this linear relationship is called an "ohmic" device. Resistors are designed to be ohmic.

To see how to apply this law in all its forms, let's watch a short video that walks through the calculations.

3. Applying the Three Forms of Ohm's Law

As the video showed, we can algebraically rearrange Ohm's Law to solve for any of the three variables. This is where you will apply the law.

The Ohm's Law Triangle

A common visual aid to remember these three forms is the Ohm's Law triangle. By covering the variable you want to find, the remaining two show you the formula.

Let's break down each case:

1. Calculating Voltage (V): If you know the current and resistance, you can find the voltage drop across the resistor.
   $V=I\times R$
   Example: A current of 2 A flows through a 10 $\Omega$ resistor. The voltage across it is $V=2\text{A}\times 10\Omega =20\text{V}$.

2. Calculating Current (I): If you know the voltage across a resistor and its resistance, you can find the current flowing through it. This is perhaps the most common use of Ohm's Law.
   $I=\frac{V}{R}$
   Example: A 12 V source is connected across a 100 $\Omega$ resistor. The current is $I=\frac{12\text{V}}{100\Omega }=0.12\text{A}$ (or 120 mA).

3. Calculating Resistance (R): If you can measure the voltage across a component and the current through it, you can determine its resistance.
   $R=\frac{V}{I}$
   Example: A light bulb has 9 V across it and draws 0.5 A of current. Its resistance is $R=\frac{9\text{V}}{0.5\text{A}}=18\Omega$.

Test your understanding!

Using the circuit diagrams below, calculate the unknown value in each case.

1. For circuit (a), find the current $I$.
2. For circuit (b), find the voltage $V$.
3. For circuit (c), find the resistance $R$.

Show answer

1. Circuit (a): We need to find current $I$. Using $I=V/R$:
   $I=\frac{12\text{V}}{3\Omega }=4\text{A}$

2. Circuit (b): We need to find voltage $V$. Using $V=I\times R$:
   $V=2\text{A}\times 5\Omega =10\text{V}$

3. Circuit (c): We need to find resistance $R$. Using $R=V/I$:
   $R=\frac{6\text{V}}{3\text{A}}=2\Omega$

4. A Practical Application: The Current-Limiting Resistor

Ohm's law is not just a theoretical exercise; it's a fundamental design tool. One of the most common applications is calculating a current-limiting resistor to protect a sensitive component, like a Light-Emitting Diode (LED).

An LED is not an ohmic device; its resistance changes with voltage. More importantly, it has a maximum current rating. Exceeding this current, even for a moment, can destroy it. We use Ohm's law to choose a resistor that guarantees the current stays at a safe level.

The logic from the article is as follows:

1. Identify the knowns:

   • Supply Voltage ($V_{supply}$): The voltage from your battery or power source (e.g., 9 V).
   • Component Voltage Drop ($V_{LED}$): The voltage the LED "uses" when it's on (e.g., 2 V for a red LED).
   • Desired Current ($I$): The safe operating current for the LED (e.g., 18 mA or 0.018 A).

2. Determine the resistor's job: The resistor needs to "get rid of" the extra voltage that the LED doesn't use. The voltage across the resistor ($V_R$) will be:
   $V_R=V_{supply}-V_{LED}$
   In the example: $V_R=9\text{V}-2\text{V}=7\text{V}$.

3. Apply Ohm's Law: Now you know the voltage across the resistor ($V_R$) and the current you want to flow through it ($I$). You can calculate the required resistance.
   $R=\frac{V_R}{I}=\frac{7\text{V}}{0.018\text{A}}\approx 389\Omega$
   Since 389 $\Omega$ is not a standard resistor value, you would choose the next common value higher (e.g., 470 $\Omega$) to be safe.

Conclusion

In this lesson, you have learned to apply Ohm's Law, the fundamental relationship between voltage, current, and resistance in an ohmic device.

Key Takeaways:

• A resistor is a component that provides a specific amount of resistance.
• Ohm's Law states that $V=I\times R$.
• This law can be rearranged to solve for voltage, current, or resistance if the other two quantities are known.
• This relationship is a critical tool for both analyzing and designing basic circuits, such as calculating a current-limiting resistor for an LED.

In our next lesson, we will revisit the concept of power from Lesson 1. You will learn how to calculate the power dissipated by a resistor. This is crucial for understanding energy consumption and for selecting resistors that can handle the heat they generate without burning out. We'll see how Ohm's Law and the power formula ($P=VI$) combine to give us even more powerful tools for analysis.