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In an R-L-C series circuit, at resonance frequency, the voltage across the resistance is:
Question

In an R-L-C series circuit, at resonance frequency, the voltage across the resistance is:

A.

much lower than applied voltage

B.

equal to applied voltage

C.

function of value of inductance

D.

much higher than applied voltage

Correct option is B

At series resonance frequency, the inductive reactance (XL) is equal to the capacitive reactance (XC):XL=XCThe impedance in an R-L-C series circuit is:Z=R2+(XLXC)2At resonance: XLXC=0, so:Z=RThe circuit’s impedance becomes purely resistive, and the total applied voltage appears across the resistance.\text{At series resonance frequency, the inductive reactance } (X_L) \text{ is equal to the capacitive reactance } (X_C): \\[6pt]X_L = X_C \\[12pt]\text{The impedance in an R-L-C series circuit is:} \\[6pt]Z = \sqrt{R^2 + (X_L - X_C)^2} \\[12pt]\text{At resonance:} \\[6pt]\bullet \, X_L - X_C = 0, \text{ so:} \\[6pt]Z = R \\[12pt]\text{The circuit's impedance becomes purely resistive, and the total applied voltage appears across the resistance.}​​

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