A resistor, an inductor, and a capacitor are connected in series to an AC source. What is the condition for resonance to occur?

The resistance must be equal to both the inductive reactance and the capacitive reactance.
The capacitive reactance must be greater than the inductive reactance.
The inductive reactance must be greater than the capacitive reactance.
The resistance must be greater than the inductive reactance.
The resistance must be greater than the capacitive reactance.
The capacitive reactance must be equal to the inductive reactance.

The given problem is based on the resonance of series connection between Resistor, inductor and capacitor. When there is a series connection between a resistor, an inductor and a capacitor, then the circuit so formed is known as the RLC circuit.

The resistances corresponding to the inductor and capacitor is known as inductive reactances and capacitive reactances. And the resonance is the condition, when the inductive and capacitive reactances becomes equal to resistance in magnitude, such they cancel the effect of each other.

So, the condition for resonance is,

[tex]R =X_{L} =X_{C}[/tex]

Here,

R is the resistance of resistor.

[tex]X_{L}[/tex] and [tex]X_{C}[/tex] are the inductive and capacitive reactances.

Thus, we can conclude that the resonance occurs when resistance becomes equal to inductive and capacitive reactances. Hence, option (A) is correct.

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