Final answer:
Decreasing either inductance (L) or capacitance (C) in an RLC circuit will increase its resonant frequency, while changing the resistance (R) does not affect the resonant frequency but influences the damping of the circuit.
Step-by-step explanation:
To answer the student’s question: Which of the following will increase the resonant frequency of an RLC circuit: a. Decrease the value of R b. Decrease the value of L c. Decrease the value of C d. Any of the above – only options b and c are correct. Decreasing the inductance (L) or the capacitance (C) will increase the resonant frequency of an RLC circuit.
The resonant frequency (f0) of an RLC circuit is given by:
f0 = 1 / (2π√(LC))
Where L is the inductance in henrys (H), and C is the capacitance in farads (F). When either L or C is decreased, the value under the square root becomes smaller, and thus the resonant frequency increases, as it is inversely proportional to the square root of the product of L and C.
Contrary to what might be initially thought, changing the resistance (R) does not affect the resonant frequency. The resistance impacts how quickly energy dissipates as thermal energy, thus affecting the bandwidth and the quality factor (Q) of the circuit, but not its resonant frequency.