In an RLC series circuit, what is the condition for resonance?

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Q: In an RLC series circuit, what is the condition for resonance?

Solution: Resonance in an RLC series circuit occurs when the inductive reactance (X_L) equals the capacitive reactance (X_C), i.e., X_L = X_C.

Steps: 6

Step 1: Understand that an RLC series circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in a single loop.
Step 2: Know that inductive reactance (X_L) is the opposition to current flow caused by the inductor, and it depends on the frequency of the current and the inductance value.
Step 3: Understand that capacitive reactance (X_C) is the opposition to current flow caused by the capacitor, and it also depends on the frequency of the current and the capacitance value.
Step 4: Recognize that resonance occurs in the circuit when the effects of the inductor and capacitor balance each other out.
Step 5: The condition for this balance is when the inductive reactance (X_L) is equal to the capacitive reactance (X_C).
Step 6: Write the condition mathematically as X_L = X_C.