What is the maximum impedance of LCR circuit?
2 Answers
In an LCR (inductor-capacitor-resistor) circuit, the maximum impedance occurs at the resonance frequency, where the inductive reactance (XL) equals the capacitive reactance (XC).
The formula for impedance \( Z \) in an LCR circuit is given by:
\[
Z = \sqrt{R^2 + (X_L - X_C)^2}
\]
At resonance, \( X_L = X_C \), so the impedance simplifies to:
\[
Z = R
\]
Thus, the maximum impedance of an LCR circuit is equal to the resistance \( R \) of the circuit when the circuit is at resonance.
The formula for impedance \( Z \) in an LCR circuit is given by:
\[
Z = \sqrt{R^2 + (X_L - X_C)^2}
\]
At resonance, \( X_L = X_C \), so the impedance simplifies to:
\[
Z = R
\]
Thus, the maximum impedance of an LCR circuit is equal to the resistance \( R \) of the circuit when the circuit is at resonance.
The maximum impedance in an LCR circuit occurs at the resonant frequency. To find it, you need to calculate the impedance of the circuit components: a resistor (R), an inductor (L), and a capacitor (C). The impedance of the circuit is given by the formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
where \( X_L = \omega L \) (inductive reactance) and \( X_C = \frac{1}{\omega C} \) (capacitive reactance).
The impedance is maximized when the difference between \( X_L \) and \( X_C \) is greatest, which happens when the circuit is far from resonance, or when \( X_L \neq X_C \). At resonance, the impedance is simply \( R \) because \( X_L = X_C \) and their effects cancel each other out.
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
where \( X_L = \omega L \) (inductive reactance) and \( X_C = \frac{1}{\omega C} \) (capacitive reactance).
The impedance is maximized when the difference between \( X_L \) and \( X_C \) is greatest, which happens when the circuit is far from resonance, or when \( X_L \neq X_C \). At resonance, the impedance is simply \( R \) because \( X_L = X_C \) and their effects cancel each other out.