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In a series RC circuit used as a high-pass filter, the input voltage delta_v_in is applied across both R and C in series, and the output voltage delta_v_out is taken across R. What is the ratio delta_v_out / delta_v_in?

1. delta_v_in / delta_v_out = R / sqrt(R² + (1/(omega*C))²)
2. delta_v_in / delta_v_out = R / sqrt(R² - (1/(omega*C))²)
3. delta_v_out / delta_v_in = R / sqrt(R² + (1/(omega*C))²)
4. delta_v_out / delta_v_in = R / sqrt(R² - (1/(omega*C))²)

Correct answer: delta_v_out / delta_v_in = R / sqrt(R² + (1/(omega*C))²)

Solution

The total impedance in series is Z = sqrt(R² + (1/omegaC)²). The current I = delta_v_in / Z. Voltage across R: delta_v_out = I*R = delta_v_in * R / Z. Thus delta_v_out / delta_v_in = R / sqrt(R² + (1/omegaC)²).

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