Final Answer:
Final Answer: The output of the given circuit is V_out = (R2 / (R1 + R2)) * V_in.
Step-by-step explanation:
In this circuit, we can see a voltage divider formed by resistors R1 and R2. The output voltage (V_out) is determined by the formula for a voltage divider, which is V_out = (R2 / (R1 + R2)) * V_in. This equation represents the fraction of the input voltage (V_in) that appears across R2. The opportunity for circuit simplification lies in recognizing the voltage divider configuration and applying the formula directly.
To further understand the derivation of the formula, consider the voltage drop across R2 as a fraction of the total voltage drop across R1 and R2. The fraction is given by the resistance of R2 divided by the total resistance (R1 + R2). This fraction is then multiplied by the input voltage (V_in) to obtain the output voltage (V_out). This analysis demonstrates how the voltage divider rule applies to the given circuit.
In conclusion, by identifying the circuit as a voltage divider and applying the corresponding formula, we determine the output voltage without the need for complex calculations. This simplification enhances our understanding of the circuit's behavior and facilitates efficient analysis in various applications.