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In an RC low-pass filter circuit, the output is taken across the capacitor C, and the input is an AC voltage of angular frequency omega. What is the ratio of output voltage to input voltage (Dv_out / Dv_in)?

1. Dv_out / Dv_in = (1/omegaC) / sqrt(R² + (1/omegaC)²)
2. Dv_in / Dv_out = (1/omegaC) / sqrt(R² - (1/omegaC)²)
3. Dv_out / Dv_in = (1/omegaC) / sqrt(R² - (1/omegaC)²)
4. Dv_in / Dv_out = (1/omegaC) / sqrt(R² + (1/omegaC)²)

Correct answer: Dv_out / Dv_in = (1/omegaC) / sqrt(R² + (1/omegaC)²)

Solution

In a series RC circuit with output across C: V_out/V_in = X_C / Z = (1/omegaC) / sqrt(R² + (1/omegaC)²). This is the standard low-pass filter transfer function magnitude.

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