Calculating Current In A Series Circuit: A Physics Problem

Hey guys! Let's dive into a classic physics problem: calculating the current in a series circuit. We've got a scenario with three resistors hooked up in a row, like little soldiers marching along a wire. Knowing how to solve this kind of problem is super important for understanding how electricity flows. We'll break it down step-by-step, making sure it's crystal clear. So, grab your calculators, and let's get started. We'll go over the basics, explain each part of the problem, and make sure you can tackle similar questions with confidence. Are you ready?

Understanding the Basics: Series Circuits

First off, what exactly is a series circuit? Imagine a single path for the electricity to flow. That's essentially what a series circuit is. Think of it like a one-lane road. All the components – in our case, the resistors – are lined up one after the other. The current, which is the flow of electrical charge, has only one route to take. This is the key characteristic of a series circuit, and it has some important implications. The most critical thing to remember is that the current is the same through every component in a series circuit. This means that if you measure the current at any point in the circuit, you'll get the same value. No matter where you stick your ammeter, the current remains constant.

Now, let's talk about the components. We have resistors, which resist the flow of current. Resistors are like speed bumps on that one-lane road, slowing down the electrical traffic. The more resistance a resistor has, the slower the current flows. The total resistance in a series circuit is simply the sum of all the individual resistances. This total resistance determines how much current will flow through the circuit when a voltage source, like a battery, is connected. Understanding this basic concept is fundamental to solving our problem.

We also need to consider the voltage source. This is the “push” that gets the electrical charges moving. The voltage source provides the energy that drives the current through the circuit. In our case, it's a 12-volt source. This means that the source is providing 12 volts of electrical potential difference. Think of it like a pump, pushing the electrical charges around the circuit. So, in summary, we've got a series circuit, resistors acting as speed bumps, a voltage source, and a constant current flowing throughout the entire system. Pretty straightforward, right?

The Problem: Calculating Current

Alright, let’s get down to brass tacks. Our problem involves a series circuit with three resistors and a voltage source. Here's what we know:

• R1 (Resistance 1) = 2 ohms (Ω)
• R2 (Resistance 2) = 4 ohms (Ω)
• R3 (Resistance 3) = 6 ohms (Ω)
• Voltage (V) = 12 volts (V)

Our mission, should we choose to accept it, is to find the current (I) that flows through each resistor. Remember, in a series circuit, the current is the same everywhere. So, once we find the current, we know it for all the resistors.

To solve this, we'll use Ohm's Law. This is the golden rule of electrical circuits. It states that the voltage (V) across a resistor is equal to the current (I) flowing through it, multiplied by the resistance (R): V = IR. We can rearrange this formula to solve for the current: I = V / R. But, before we can use this, we need to figure out the total resistance of the entire circuit. That's the next step, and it is pretty easy to do since the resistors are in series. Are you with me so far?

Step-by-Step Solution: Finding the Current

Here’s how we're going to solve this problem step-by-step, making it super clear. This way, you can easily follow along and understand how we get the answer. We will solve using the given information to find the current that passes through each resistor.

Step 1: Calculate the Total Resistance (R_total)

As we mentioned earlier, the total resistance in a series circuit is just the sum of all individual resistances. So, to find R_total, we add up R1, R2, and R3:

R_total = R1 + R2 + R3 R_total = 2 Ω + 4 Ω + 6 Ω R_total = 12 Ω

Great! We now know the total resistance of the circuit is 12 ohms.

Step 2: Calculate the Current (I)

Now we'll use Ohm's Law (I = V / R) to find the current. We know the total voltage (V = 12 V) and the total resistance (R_total = 12 Ω).

I = V / R_total I = 12 V / 12 Ω I = 1 A

There you have it! The current flowing through the circuit is 1 amp (A). Since it's a series circuit, this 1 amp flows through each of the resistors. So, the answer is 1 A, but that is not one of the choices. Let's make sure we solved the problem properly!

Recap: First, we found the total resistance by adding up all the individual resistors in the circuit, which was 12 ohms. Then, we used Ohm’s Law, dividing the total voltage (12 volts) by the total resistance (12 ohms), giving us a current of 1 amp. The current is the same across all resistors.

Addressing the Answer Choices

Let's go back and check our answer choices to make sure we got the current that passes through each resistor. Our calculated answer is 1 A, but that is not among the options. However, let us review each of the answer choices given to find out what is going on:

a. 2.5 A. b. 3 A. c. 2 A.

Now that we have reviewed all the answer choices, we realize that there might be a typo and our calculated value is not present in the possible solutions. Since the question asks