Without a specific circuit diagram or more information about the op-amp and switches, it's difficult to provide a specific answer. However, we can provide some general information on how to use the ideal op-amp model to determine the gain for a given circuit configuration.
In general, the ideal op-amp model assumes that the op-amp has infinite input impedance, zero output impedance, infinite open-loop gain, and zero input bias current. Using this model, we can analyze the circuit by assuming that the voltage at the inverting and non-inverting inputs of the op-amp are equal, and then applying Kirchhoff's laws to determine the voltage gain.
For a circuit with two single-pole single-throw (SPST) switches, there are four possible configurations depending on whether each switch is open or closed. To determine the gain for a specific configuration, we need to analyze the circuit and determine the voltage at the output (υ0) divided by the voltage at the input (υs).
Assuming that s1 is closed and s2 is open, we can analyze the circuit as follows:
- When s1 is closed, the input voltage υs is connected directly to the inverting input of the op-amp.
- Since s2 is open, the non-inverting input of the op-amp is connected to ground.
- Therefore, the voltage at the inverting and non-inverting inputs of the op-amp are equal, and we can assume that the inverting input is at ground potential.
- Since the op-amp has infinite open-loop gain, the output voltage υ0 will adjust itself so that the inverting input remains at ground potential.
- Therefore, the output voltage υ0 will be zero, and the gain G = υ0/υs is also zero.
So for this specific configuration, the gain is zero.