Frequency effect on parallel RC: As the source frequency decreases in a parallel RC circuit, what happens to the total impedance seen by the source?

Introduction / Context:
Understanding how impedance varies with frequency is essential in filter design and AC network analysis. In a parallel RC circuit, the capacitor branch admittance depends directly on frequency; therefore, the overall impedance is frequency-sensitive in a predictable way.

Given Data / Assumptions:

• Parallel combination: resistor R in parallel with capacitor C.
• Ideal components; focus on steady-state sinusoidal behavior.
• We vary frequency f downward and observe total impedance Z_total.

Concept / Approach:
Admittance of the capacitor is Y_C = jωC (magnitude ωC), which decreases as frequency decreases (since ω = 2πf). The total admittance of the parallel network is Y_total = 1/R + jωC. As ω decreases, |Y_total| decreases toward 1/R, causing the total impedance Z_total = 1 / |Y_total| to increase toward R.

Step-by-Step Solution:

Verification / Alternative check:
Limiting cases: At very low f, capacitor behaves like open circuit → Z_total ≈ R (highest). At very high f, capacitor admittance dominates → Z_total becomes small (lowest). This trend confirms impedance increases as frequency decreases.

Why Other Options Are Wrong:

• Decreases / decreases to zero: Opposite to actual behavior as f is reduced.
• Does not change: Incorrect because the capacitive branch is frequency dependent.

Common Pitfalls:

• Confusing series and parallel behavior; series RC magnitude generally increases with frequency due to X_C decreasing, but the parallel case must be reasoned via admittance.

Final Answer:
increases