Question

Consider the circuit with an ideal OPAMP shown in the figure. 
Assuming \( |V_{IN}| \ll |V_{CC}| \) and \( |V_{REF}| \ll |V_{CC}| \), the condition at which \( V_{OUT} \) equals to zero is

• A. \( V_{IN} = V_{REF} \)
• B. \( V_{IN} = 0.5 \, V_{REF} \)
• C. \( V_{IN} = 2 \, V_{REF} \)
• D. \( V_{IN} = 2 + V_{REF} \)

Hint:

For an ideal op-amp with feedback, the output voltage is zero when the non-inverting input is at the same potential as the inverting input.

Answer 1

The Correct Option is A

This is a feedback circuit with an ideal operational amplifier (op-amp). For the output voltage \( V_{OUT} \) to be zero, the input voltage \( V_{IN} \) must balance the reference voltage \( V_{REF} \) in such a way that the inverting input of the op-amp is at the same potential as the non-inverting input. Since \( |V_{IN}| \ll |V_{CC}| \) and \( |V_{REF}| \ll |V_{CC}| \), for the op-amp to output zero voltage, the relationship between \( V_{IN} \) and \( V_{REF} \) should satisfy: \[ V_{IN} = V_{REF}. \] Thus, the correct answer is (A). Final Answer: \( V_{IN} = V_{REF} \)