The given problem involves calculating the voltage gain of an inverting operational amplifier (op-amp) circuit. Let's solve this step-by-step.

Given:

• Open loop gain of the op-amp \( A_0 = 10^5 \).
• Input resistance \( R_1 = 5 \, \text{k}\Omega \).
• Feedback resistance \( R_f = 100 \, \text{k}\Omega \).

Formula for Closed Loop Gain of Inverting Amplifier:

The voltage gain \( A_v \) for an inverting amplifier is given by the formula:

\(A_v = -\frac{R_f}{R_1}\)

Substituting the values:

\(A_v = -\frac{100 \, \text{k}\Omega}{5 \, \text{k}\Omega} = -20\)

Since the open-loop gain is very high, the effect on the closed loop gain is minimal, and it can be approximately considered equal to the calculated value above.

However, for higher precision, the closed-loop gain with feedback can be better expressed taking the op-amp gain into account.

Formula Considering Open Loop Gain:

The effective gain considering the high gain \( A_0 \) is given by:

\(A_{\text{closed-loop}} = \frac{A_v}{1 + \frac{A_v}{A_0}}\)

Substituting the values:

• \(A_v = -20\)

\(A_{\text{closed-loop}} = \frac{-20}{1 + \frac{-20}{10^5}}\)

Upon calculation:

\(A_{\text{closed-loop}} \approx -16.67\)

Conclusion:

The voltage gain of the circuit is approximately \(-16.67\), which matches the correct answer.