Effect of shunt resistance on a parallel resonant circuit: If the resistance in parallel with a parallel resonant network is reduced, what happens to the bandwidth?

Introduction / Context:Parallel (tank) resonant circuits have a bandwidth that depends on the effective parallel resistance R_p and the capacitance/inductance values. Knowing how bandwidth changes with R_p is essential for controlling selectivity and Q in RF and filter designs.

Given Data / Assumptions:

• Parallel resonant circuit with an effective shunt resistance R_p.
• Ideal L and C; focus on the effect of changing R_p.

Concept / Approach:The -3 dB bandwidth of a parallel resonant circuit is BW = 1 / (2π C R_p) (equivalently BW = R_p / (2π L Q_p) relationships lead to the same conclusion). Thus BW is inversely proportional to R_p. Reducing R_p increases admittance (loss), which broadens the response and increases bandwidth.

Step-by-Step Reasoning:

Verification / Alternative check:In the limit R_p → ∞ (no loss), the tank has very high Q and vanishingly small BW. As R_p is reduced, the peak flattens and widens, precisely the definition of increased bandwidth.

Why Other Options Are Wrong:

• Decreases / becomes sharper: Opposite of the effect of adding loss in parallel.
• Disappears: Resonance still exists, but it becomes broader and less pronounced.

Common Pitfalls:

• Confusing series and parallel bandwidth relationships; the dependence on resistance is inverted between the two forms.

Final Answer:increases