(i) Design a non-inverting amplifier having a gain of 50 . Draw the circuit [ 4 pts .] and indicate the value of any components used [ 4 pts .]. (Use resistor values between \( 1 \mathrm{k} \Omega \) and \( 500 \mathrm{k} \Omega \).)

To design a non-inverting amplifier with a gain of 50, you can use the formula for gain \( A_v = 1 + \frac{R_f}{R_{in}} \). Rearranging for \( R_f \) gives you: \[ R_f = R_{in} \cdot (A_v - 1) \] Assuming \( R_{in} = 1 \, \text{k}\Omega \): \[ R_f = 1 \, \text{k}\Omega \cdot (50 - 1) = 49 \, \text{k}\Omega \] This can be achieved with a combination of resistors. For example, use \( R_{in} = 1 \, \text{k}\Omega \) and \( R_f = 47 \, \text{k}\Omega + 2 \, \text{k}\Omega \) (with 47 kΩ and a 2 kΩ resistor in series). The circuit diagram would look like this: ``` +Vcc | --- | | | | --------| |----------- | | --- | | Rf | |---------- Output (Vout) | --- | | | | --------| |----------- | | --- | | Rin | |---------- Input (Vin) | GND ``` In this circuit, \( R_{in}\) is connected to the input voltage and \( R_f\) connects from the output to the non-inverting input. Make sure to remember to connect the operational amplifier (op-amp) according to the standard non-inverting amplifier configuration with proper power supply connections.