When an LRC series circuit is driven at resonance, which of the following statements about the circuit are correct? (There may be more than one correct choice.)a) The impedance of the circuit has its minimum value.b) The inductive reactance and the capacitive reactance are exactly equal to each other.c) The impedance of the circuit is zero.d) The inductive reactance and the capacitive reactance are both zero.e) The impedance of the circuit has its maximum value.

Recall that the resonance in an LRC circuit occurs when the current through the circuit is at its maximum, and such takes place when the impedance (Z) of the circuit reaches its maximum. This means that the impedance (see formula below) is at its minimum value:

[tex]Z=\sqrt{R^2+(\omega\,L-\frac{1}{\omega\,C})^2 }[/tex]

as per the impedance expression above, such happens when the term in parenthesis inside the root which contains the inductive reactance ([tex]\omega\,L[/tex]) and the capacitive reactance ([tex]1/\omega\,C[/tex]) have the same value.

Therefore, answers:

a) "The impedance of the circuit has its minimum value."

and

b) "The inductive reactance and the capacitive reactance are exactly equal to each other."

are correct answers.

onyebuchinnaji onyebuchinnaji · Answer 2 · 2021-12-02T12:58:54+01:00

(a) The impedance of the circuit has its minimum value.

(b) The inductive reactance and the capacitive reactance are exactly equal to each other

LRC series circuit consists of inductor, resistor and capacitor is series.

The impedance of the circuit is calculated as follows;

[tex]Z = \sqrt{R^2 + (X_C -X_L)^2}[/tex]

where;

R is the resistance
[tex]X_C[/tex] is the capacitive reactance
[tex]X_L[/tex] is the inductive reactance

The impedance of the circuit is minimum when the capacitive reactance is equal to the inductive reactance.

[tex]X_C = X_L \\\\Z = \sqrt{R^2 \ + (0)^2} \\\\Z = R[/tex]

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