Question
Download Solution PDFAn inductor and a capacitor are connected in an A.C. circuit inductance and capacitance are 1 H and 25μF then for maximum current, the angular frequency will be (the circuit is connected in series):
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- The ac circuit containing the capacitor, resistor, and the inductor is called an LCR circuit.
- For a series LCR circuit, the total potential difference of the circuit is given by:
\(V = \sqrt {{V_R^2} + {{\left( {{V_L} - {V_C}} \right)}^2}} \)
Where VR = potential difference across R, VL = potential difference across L and VC = potential difference across C
- For a series LCR circuit, Impedance (Z) of the circuit is given by:
\(\)\(Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} \)
Where R = resistance, XL =induvtive reactance and XC = capacitive reactive
- The resonant frequency of a series LCR circuit is given by
\(⇒ ν =\frac{1}{2π\sqrt{LC}}\)
where L = inductance and C = capacitance
CALCULATION:
Given L = 1H and C = 25μF
⇒ ω = 2πν -----(2)
From equation 1 and equation 2,
⇒ ω = 200 rad/sec
- Hence, option 1 is correct.
Last updated on Jul 4, 2025
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