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In an RLC circuit, resonance frequency is a particular frequency where the circuit responds most efficiently to an external voltage. At this frequency, the inductive reactance and capacitive reactance are equal and cancel each other out. This results in the impedance being purely resistive, calculated only with the resistor value, which maximizes current flow.
To calculate the resonance frequency \( f \) in an RLC circuit, you use the formula:

• \( f = \frac{1}{2\pi \sqrt{LC}} \)

Where \( L \) is inductance in henries and \( C \) is capacitance in farads.Plug in the circuit values \( L = 0.750 \text{ H} \) and \( C = 0.0180 \times 10^{-6} \text{ F} \), then calculate to find \( f \). This results in \( f \approx 1.374 \times 10^3 \text{ Hz} \) for the original setup. A change in capacitance and thus the recalculated frequency can impact circuit performance by altering the point of resonance, as we see when the capacitance changes to \( C = 0.0360 \mu \text{F} \), giving a new frequency of \( f' \approx 0.950 \times 10^3 \text{ Hz} \).
Understanding resonance is crucial because it determines the conditions under which the circuit operates most efficiently.

Power factor in an AC circuit describes the efficiency of power usage. It is defined as the cosine of the phase angle \( \phi \) between voltage and current. The formula is:

• Power Factor (PF) = \( \cos \phi \)

In an RLC circuit, when the power factor is 1, the circuit is said to be at resonance. This means all power supplied by the source is effectively used. This ideal situation happens when inductive and capacitive reactances cancel, leading to voltage and current being perfectly in phase.
In our given exercise, since the power factor at resonance is calculated as 1, the circuit is using energy most effectively. This implies there's minimal reactive power (the power that bounces between source and reactive components without doing actual work), achieving maximum real power usage.
This optimal condition not only saves energy costs but also includes other benefits, like reduced heating and prolonged lifespan for the components used.

Average power in an AC circuit signifies the power actually consumed or converted into work. For a series RLC circuit at resonance, average power \( P \) can be represented by:

• \( P = \frac{V^2}{R} \)

Here, \( V \) is the voltage amplitude supplied by the source, and \( R \) is the resistance. Substitute \( V = 150 \text{ V} \) and \( R = 150 \Omega \) into the formula to find \( P \). This gives an average power output of 150 W.
Even when the circuit's capacitance changes, resulting in a new resonance frequency, the average power calculation remains unchanged if the circuit remains at resonance. Therefore, with a new capactior or frequency adjustment as seen here, the average power still equals 150 W.
Understanding average power is essential in designing efficient electrical systems as it directly affects the cost of electricity and engineering requirements of electrical systems.