Question

For the input voltage \( V_i = (200 \, \text{mV}) \sin (400t) \), the amplitude of the output voltage \( V_0 \) of the given OPAMP circuit is ............. V. 

Hint:

In an OPAMP circuit, the output voltage is the product of the gain and the input voltage. Calculate the gain from the resistor values and apply it to find the output.

Answer 1

Correct Answer: 11

Step 1: Analyze the given OPAMP circuit.
The circuit consists of three operational amplifiers, each with resistors \( R_1, R_2, R_3, R_f \). The configuration is likely to be a non-inverting amplifier, which has the voltage gain \( A \) given by: \[ A = 1 + \frac{R_f}{R_1} \] The output voltage \( V_0 \) is related to the input voltage \( V_i \) by: \[ V_0 = A \times V_i = \left( 1 + \frac{R_f}{R_1} \right) \times V_i \] where \( V_i = (200 \, \text{mV}) \sin(400t) \).
Step 2: Determine the values of \( R_f \) and \( R_1 \).
Given that the resistances in the circuit are all equal (\( R_1 = R_2 = R_3 = 10 \, \text{k}\Omega \) and \( R_f = 35 \, \text{k}\Omega \)), we can calculate the voltage gain: \[ A = 1 + \frac{35 \, \text{k}\Omega}{10 \, \text{k}\Omega} = 1 + 3.5 = 4.5 \]
Step 3: Calculate the output voltage.
Substitute the value of \( A \) and \( V_i \) into the equation for \( V_0 \): \[ V_0 = 4.5 \times (200 \, \text{mV}) = 900 \, \text{mV} \] The amplitude of the output voltage is 200 V.