1.1 Find the relationship between V and V in circuits a and b of figure 1 assuming b) a) R R mmm Vout - Vout ideal op-amps Figure 1: a) Op-amp with capacitor and b) op-amp with an inductor. 1.2 AssumeV (t) = A sin(20ft). Using the formula in part 1.1, simplify Vand report the maximum value of V out °Ţ₁
1.1 Find the relationship between V and V in circuits a and b of figure 1 assuming b) a) R R mmm Vout - Vout ideal op-amps Figure 1: a) Op-amp with capacitor and b) op-amp with an inductor. 1.2 AssumeV (t) = A sin(20ft). Using the formula in part 1.1, simplify Vand report the maximum value of V out °Ţ₁
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![### Understanding Op-Amp Circuits
#### 1.1 Analysis
We aim to find the relationship between \( V_{out} \) and \( V_{in} \) in circuits a and b shown in Figure 1, assuming ideal operational amplifiers (op-amps).
- **Figure 1a: Op-Amp with Capacitor**
This circuit includes:
- A resistor \( R \) connected in series after an input voltage \( V_{in} \).
- A capacitor \( C \) connected in parallel with the op-amp.
- The output voltage \( V_{out} \) is taken from the op-amp.
- **Figure 1b: Op-Amp with Inductor**
This circuit includes:
- A resistor \( R \) connected in series after an input voltage \( V_{in} \).
- An inductor \( L \) connected in parallel with the op-amp.
- The output voltage \( V_{out} \) is taken from the op-amp.
#### Figure Description
- **Ideal op-amps**: The op-amps are assumed to be ideal in this problem.
#### 1.2 AC Signal Analysis
Given:
\[ V_{in} (t) = A_{in} \sin(2\pi ft) \]
Using the formula derived in part 1.1, we will:
1. Simplify \( V_{out} \).
2. Report the maximum value of \( V_{out} \).
This problem involves applying AC analysis, where the input voltage is a sinusoidal function. The detailed steps would involve solving the differential equations governing the circuits and applying the properties of ideal op-amps to determine \( V_{out} \).
The maximum value of \( V_{out} \) would generally correspond to the amplitude of the resultant output sine wave derived from the analysis. The exact calculations and results depend on the specific relationships found from part 1.1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a579a7f-99c6-465f-8352-06e32f8837ce%2F61803182-d8e3-49d3-9b48-2ed45d56a8de%2F03lv5em_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Op-Amp Circuits
#### 1.1 Analysis
We aim to find the relationship between \( V_{out} \) and \( V_{in} \) in circuits a and b shown in Figure 1, assuming ideal operational amplifiers (op-amps).
- **Figure 1a: Op-Amp with Capacitor**
This circuit includes:
- A resistor \( R \) connected in series after an input voltage \( V_{in} \).
- A capacitor \( C \) connected in parallel with the op-amp.
- The output voltage \( V_{out} \) is taken from the op-amp.
- **Figure 1b: Op-Amp with Inductor**
This circuit includes:
- A resistor \( R \) connected in series after an input voltage \( V_{in} \).
- An inductor \( L \) connected in parallel with the op-amp.
- The output voltage \( V_{out} \) is taken from the op-amp.
#### Figure Description
- **Ideal op-amps**: The op-amps are assumed to be ideal in this problem.
#### 1.2 AC Signal Analysis
Given:
\[ V_{in} (t) = A_{in} \sin(2\pi ft) \]
Using the formula derived in part 1.1, we will:
1. Simplify \( V_{out} \).
2. Report the maximum value of \( V_{out} \).
This problem involves applying AC analysis, where the input voltage is a sinusoidal function. The detailed steps would involve solving the differential equations governing the circuits and applying the properties of ideal op-amps to determine \( V_{out} \).
The maximum value of \( V_{out} \) would generally correspond to the amplitude of the resultant output sine wave derived from the analysis. The exact calculations and results depend on the specific relationships found from part 1.1.
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