Electric Potential At Point C: A Calculation Guide

Hey guys! Today, we're diving into the fascinating world of electrical circuits and tackling a problem that often pops up: determining the electric potential at a specific point. Specifically, we'll be figuring out the electric potential at point C in a given circuit. Don't worry, it might sound intimidating, but we'll break it down step by step, making it super easy to understand. We'll be using some basic principles of electrical circuits, and I promise, by the end of this, you'll feel confident in solving similar problems.

So, what exactly is electric potential? Think of it like this: It's the amount of potential energy that a unit of electric charge has at a specific point in a circuit. It's measured in volts (V), and it's super important because it tells us how much 'push' the electric charge has at that point. The higher the electric potential, the more 'push' there is. Understanding electric potential helps us analyze how current flows through a circuit, which is crucial for designing and troubleshooting electrical systems. We'll start by taking a look at the given information, then gradually apply the necessary concepts to arrive at the solution. Let's start with the basics, we have two voltage sources, some resistors and we will calculate the electric potential at point C. Ready? Let's go!

To be successful, we need to apply some of the most fundamental concepts to understand the problem. The main concept here is Ohm's Law and its relationship with the voltage drop in the circuit. But don't worry, we'll review all the concepts you need to solve it in a very easy way. Furthermore, we must understand the direction of the current flow, which helps us to calculate the value of the potential at point C. Finally, we'll make sure that we understand the steps to arrive at the correct solution. Let's start by looking at the specific problem we're going to solve. First, we'll analyze the circuit, and then, using our knowledge of the electrical components, we'll find the answer! Let's get started!

Understanding the Circuit and the Given Information

Alright, let's take a look at the circuit diagram provided. We have a circuit with two voltage sources and two resistors. Here's a quick rundown of the components and their values:

• Voltage Sources: We have a voltage difference of $30V - 21V$. This is an essential value that we will use to calculate the electric potential at point C.
• Resistors: There are two resistors in the circuit. One resistor has a resistance of $3 ext{ } m ext{Ω}$ and the other has a resistance of $5 ext{ } m ext{Ω}$. Resistors are very important because they oppose the flow of current.

The goal is to determine the electric potential at point C. Remember, electric potential is a measure of the electric potential energy per unit charge at a point in an electric field. This means we are trying to determine how much “energy” a charge would have if it were placed at point C. This is a very important concept that can be used in other applications. Now that we have a solid understanding of the circuit, let's go on to the next step, which involves using Ohm's Law and calculating the current flowing through the circuit. We have all the information that we need. So, what are we waiting for? Let's get to work!

Analyzing the Circuit Components

Let's break down the components of the circuit and talk about their roles. The voltage sources are the power supply, pushing the electric current through the circuit. The resistors, on the other hand, are the elements that impede the flow of current. When the current flows through a resistor, there's a drop in the electric potential, which is also known as voltage drop. This voltage drop is directly proportional to the current and the resistance value, according to Ohm's Law. In this circuit, the resistors are likely connected in series or in parallel, which affects how the current flows and how the voltage drops across them. The resistors will determine how the current flows in the circuit. The voltage drop at the resistors will determine the electric potential at point C.

Applying Ohm's Law and Calculating the Current

Now, let's get into the core of the problem: calculating the current. This is where Ohm's Law comes into play, a fundamental concept in electrical circuits. Ohm's Law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) between them. The formula is: $V = I imes R$.

First, we need to calculate the total voltage in the circuit. In this case, we have: $30V - 21V = 9V$. This is our total voltage drop for the circuit. Now, we must calculate the total resistance of the circuit. The resistors are in series, so we can calculate the equivalent resistance by summing the individual resistances: $3 ext{ } m ext{Ω} + 5 ext{ } m ext{Ω} = 8 ext{ } m ext{Ω}$. The total resistance of the circuit is $8 ext{ } m ext{Ω}$.

We can rearrange Ohm's Law to solve for the current: $I = V / R$. With the total voltage of 9V and a total resistance of 8 Ω, the current is $I = 9V / 8 ext{ } m ext{Ω} = 1.125A$. The current through the circuit is 1.125A. Great job! We're making progress. Now that we know the current, we can calculate the voltage drop across each resistor, and finally, we can determine the electric potential at point C. Ready for the next step?

Voltage Drop Across Resistors

Once we have the value of the current, we can calculate the voltage drop across each resistor in the circuit. We use Ohm's Law to do this, $V = I imes R$. For the 3 Ω resistor, the voltage drop is $V = 1.125A imes 3 ext{ } m ext{Ω} = 3.375V$. For the 5 Ω resistor, the voltage drop is $V = 1.125A imes 5 ext{ } m ext{Ω} = 5.625V$. Remember, this voltage drop is what reduces the electric potential as the current flows through the resistor. The direction of the current flow also determines the electric potential at point C. To calculate the electric potential at point C, we will apply all the concepts that we have learned. Let's move to the next section to get the answer!

Determining the Electric Potential at Point C

Finally, we're at the point where we can determine the electric potential at point C! This is where all our previous calculations come together. To find the electric potential at point C, we need to consider the voltage drops across the resistors and the direction of the current flow. Keep in mind that electric potential is relative; we often measure it with respect to a reference point (usually ground, which is 0V). The electric potential at point C will depend on where in the circuit point C is. If point C is located at the end of the first resistor, we'll consider the voltage drop of the first resistor. If point C is located at the end of the second resistor, we'll consider the voltage drops of both resistors. Now, let's analyze the given options to find the answer. The value of the potential must be one of the answers.

Analyzing the Results

From the circuit analysis, we know the following:

• Total Voltage: 9V.
• Current: 1.125A.
• Voltage drop across the $3 ext{ } m ext{Ω}$ resistor: $3.375V$.
• Voltage drop across the $5 ext{ } m ext{Ω}$ resistor: $5.625V$.

If we assume that point C is located after the $3 ext{ } m ext{Ω}$ resistor, we subtract the voltage drop from the total voltage: $9V - 3.375V = 5.625V$. If we assume that point C is located after the $5 ext{ } m ext{Ω}$ resistor, we subtract the voltage drops of both resistors from the total voltage: $9V - 3.375V - 5.625V = 0V$. However, the electric potential is usually not 0V. The closest result from the options is 6V. Therefore, the answer is option B.

The Answer

Based on our calculations and the analysis of the options, the electric potential at point C is B) 6V. Congrats, guys! You successfully solved the problem. You've demonstrated your understanding of electric potential, Ohm's Law, and how to analyze a basic electrical circuit. Keep practicing, and you'll become a pro in no time.

I hope this step-by-step guide helped you understand how to solve this kind of electrical circuit problem. Remember, the key is to break down the problem into smaller parts and apply the fundamental concepts. See you next time! Feel free to ask any other questions! Goodbye!