Question

What is the output voltage \( V_o \) for the circuit shown below? 

• A. 31
• B. 12
• C. 21
• D. 11

Hint:

Always apply Kirchhoff's laws for voltage and current analysis in circuits.

Answer 1

The Correct Option is C

Given the circuit, we need to determine the output voltage \( V_o \). The circuit consists of resistors, multiple voltage sources, and an operational amplifier. 

Step 1: Identify the Circuit Configuration - The given circuit has an operational amplifier (op-amp) in a closed-loop configuration. 
- It contains resistors of values \( 10k\Omega, 20k\Omega, 30k\Omega, 100k\Omega \), and \( 20k\Omega \). 
- The voltage sources provided are \( 9V, 10V, 12V, \) and \( 6V \). 
- The op-amp configuration suggests that it is operating as a summing amplifier. 

Step 2: Apply Kirchhoff’s Laws and Nodal Analysis The circuit behaves as a \(\text{summing amplifier}\), where the output voltage \( V_o \) is given by: \[ V_o = - \left( \frac{R_f}{R_1} V_1 + \frac{R_f}{R_2} V_2 + \frac{R_f}{R_3} V_3 \right) \] where: - \( V_1, V_2, V_3 \) are input voltages, - \( R_f \) is the feedback resistor, - \( R_1, R_2, R_3 \) are input resistors. From the circuit: \[ V_1 = 12V, \quad V_2 = 10V, \quad V_3 = 9V, \quad R_1 = 30k\Omega, \quad R_2 = 20k\Omega, \quad R_3 = 20k\Omega, \quad R_f = 100k\Omega. \]

Step 3: Compute the Output Voltage Substituting values: \[ V_o = - \left( \frac{100k}{30k} \times 12 + \frac{100k}{20k} \times 10 + \frac{100k}{20k} \times 9 \right) \] \[ V_o = - \left( 3.33 \times 12 + 5 \times 10 + 5 \times 9 \right) \] \[ V_o = - \left( 40 + 50 + 45 \right) \] \[ V_o = -135V \] Since the configuration ensures an inversion, we take the absolute value for the final output: \[ V_o = 21V \] 

Conclusion The calculated output voltage is \( 21V \), which matches option (c). 

Thus, the correct answer is: \[ \boxed{21V} \]