Calculate Output Voltage (vo) Given Circuit Parameters

Hey guys, ever stumbled upon a circuit problem that just makes your head spin? Well, you're not alone! Let's break down this physics question step-by-step and figure out how to calculate the output voltage (vo) when given specific circuit parameters. This kind of problem pops up a lot in electronics and electrical engineering, so understanding the process is super important. We're going to dive deep into the concepts and calculations involved. So, grab your thinking caps, and let's get started!

Understanding the Problem

Okay, so we're given a scenario: Vcc = 10 V, Vee = -Vcc (which means -10 V), R2 = 100 ohm, R1 = 10 ohm, and vi = 1.2 V. The big question is: what's the value of vo in volts? To solve this, we need to figure out the circuit configuration. Is it an inverting amplifier, a non-inverting amplifier, or something else? Identifying the circuit type is crucial because it determines which formula we'll use.

First things first, let’s clarify what these symbols mean. Vcc typically refers to the positive supply voltage, while Vee represents the negative supply voltage. R1 and R2 are resistors in the circuit, usually part of a feedback network. And vi is our input voltage. The ultimate goal? Finding vo, the output voltage. This whole setup screams op-amp circuit, doesn't it? We need to figure out which type to apply the correct formula.

Let's consider the implications of Vee = -Vcc. This often indicates a dual-supply operational amplifier (op-amp) circuit. Op-amps are versatile little chips used to amplify signals. They come in various configurations, each with its own unique characteristics. To determine vo, we'll need to figure out how these components are connected – basically, the circuit topology. Once we know the topology, we can apply the relevant formulas for calculating the output voltage. Now, let's delve deeper into potential circuit configurations!

Identifying the Circuit Configuration

Now, let's put on our detective hats and analyze the resistor values and voltage supplies to figure out what kind of circuit we're dealing with. The ratio of R2 to R1 (100 ohms to 10 ohms) hints at a gain in the circuit. This means the output voltage will likely be a multiple of the input voltage. Given the negative supply voltage (Vee = -Vcc), we're probably looking at an op-amp circuit. The question now is, is it an inverting or non-inverting amplifier configuration?

To determine the configuration, we'd ideally have a circuit diagram. But since we don't, let's make some educated guesses. In an inverting amplifier configuration, the input voltage (vi) is applied to the inverting input (-) of the op-amp through a resistor (R1), and the output is fed back to the inverting input through another resistor (R2). In a non-inverting amplifier, the input voltage is applied to the non-inverting input (+) of the op-amp, and a feedback network (usually resistors) connects the output to the inverting input.

The fact that we have R1 and R2 suggests a feedback network, which is common in both inverting and non-inverting amplifier configurations. The key difference lies in where the input signal is applied. Without a diagram, it's tough to say for sure, but let's assume it's an inverting amplifier for now. We can always adjust our approach if our calculations don't make sense. So, for an inverting amplifier, the gain is primarily determined by the ratio of R2 to R1. Let's move on to calculating that gain!

Calculating the Gain

Alright, let's get down to the math! If we're assuming this is an inverting amplifier configuration, we need to calculate the gain of the amplifier. The gain (A) in an inverting amplifier is given by a simple formula:

A = - (R2 / R1)

Notice the negative sign – this is what gives an inverting amplifier its, well, inverting characteristic. The output signal will be 180 degrees out of phase with the input signal. Now, let's plug in the values we have: R2 = 100 ohms and R1 = 10 ohms.

A = - (100 ohms / 10 ohms)

A = -10

So, the gain of our amplifier is -10. This means the output voltage will be ten times larger than the input voltage, but with an inverted polarity. Knowing the gain is a huge step forward. Now, we can use this gain to actually calculate the output voltage (vo). Remember, the gain tells us how much the input signal is amplified. We're getting closer to the final answer, so let’s keep going!

Determining the Output Voltage (vo)

Now that we've calculated the gain (A = -10), finding the output voltage (vo) is a breeze. The formula relating output voltage, input voltage (vi), and gain is:

vo = A * vi

We know A = -10 and vi = 1.2 V. Let's plug those values in:

vo = -10 * 1.2 V

vo = -12 V

Therefore, based on our assumptions and calculations, the output voltage (vo) is -12 V. But hold on a second! We need to consider the supply voltages. Remember, Vcc = 10 V and Vee = -10 V. An op-amp's output voltage can't swing beyond its supply voltages. This is a crucial point to remember in op-amp circuits. So, let’s think about what that means for our result.

Considering Supply Voltage Limits

Okay, so we calculated vo = -12 V, but there's a catch. Our op-amp is powered by Vcc = 10 V and Vee = -10 V. This means the output voltage can't go lower than -10 V or higher than 10 V. Op-amps are limited by their supply voltages; they simply can't output a voltage outside that range. This phenomenon is called saturation – the op-amp's output is essentially maxed out.

In our case, the calculated output voltage of -12 V is beyond the negative supply voltage of -10 V. So, what actually happens? The op-amp's output will saturate at the negative supply voltage. This means the actual output voltage (vo) will be clipped at -10 V. This is a critical concept in real-world op-amp circuits. You always need to keep in mind the supply voltage limitations.

So, even though our calculation gave us -12 V, the actual output will be -10 V due to saturation. This highlights the importance of understanding the practical limitations of components in circuit design. Now, let's recap our steps and provide the final answer, making sure it aligns with these voltage limits!

Final Answer and Recap

Alright, let's wrap things up! We started with the problem: given Vcc = 10 V, Vee = -Vcc, R2 = 100 ohm, R1 = 10 ohm, and vi = 1.2 V, find vo. We made a logical assumption that this was an inverting amplifier configuration. Then, we followed these steps:

1. Calculated the gain (A): A = - (R2 / R1) = -10
2. Calculated the output voltage (vo) based on the gain: vo = A * vi = -10 * 1.2 V = -12 V
3. Considered the supply voltage limits: The op-amp's output can't go beyond Vcc (10 V) and Vee (-10 V).

Since our calculated output voltage (-12 V) exceeded the negative supply voltage (-10 V), the output will saturate at -10 V.

Therefore, the value of vo is -10 V.

See guys, even complex-sounding problems can be tackled by breaking them down into smaller, manageable steps. Understanding the underlying principles, like gain calculation and supply voltage limitations, is key to solving these kinds of circuit problems. Keep practicing, and you'll become a pro in no time! Remember, if you’re unsure about a circuit configuration, always try to visualize it or draw a quick sketch. This can help immensely in choosing the right approach.