RC network identification — high-pass or low-pass?: Consider a simple RC with a series capacitor feeding a resistor to ground; the output is taken across the resistor. Is this a first-order high-pass filter?

Introduction / Context:Recognizing canonical RC topologies is essential for quick design judgements. Two complementary first-order forms exist: RC low-pass (R in series, C to ground, output across C) and RC high-pass (C in series, R to ground, output across R).

Given Data / Assumptions:

• Series capacitor C from input node to output node.
• Resistor R from output node to ground.
• Output measured across R; linear, time-invariant operation.

Concept / Approach:For the series-C / shunt-R network, the transfer magnitude |H(jω)| = |V_out/V_in| increases with frequency: |H| = ωRC / √(1 + (ωRC)^2). At low frequency (ω → 0), the capacitor blocks, |H| → 0. At high frequency (ω → ∞), the capacitor is a short, |H| → 1. This is precisely the behavior of a first-order high-pass filter, with cutoff f_c = 1/(2πRC).

Step-by-Step Solution:

Verification / Alternative check:Bode plot shows +20 dB/decade slope below f_c and flat passband above f_c; phase approaches +90 degrees at high frequency.

Why Other Options Are Wrong:

Common Pitfalls:Confusing where the output is taken; swapping where you probe flips high-pass vs low-pass.

Final Answer:Yes, it is a first-order high-pass filter