Join WhatsApp Icon JEE WhatsApp Group
Question 17

For a series LCR circuit with $$R = 100$$ $$\Omega$$, $$L = 0.5$$ mH and $$C = 0.1$$ pF connected across 220 V - 50 Hz AC supply, the phase angle between current and supplied voltage and the nature of the circuit is:

For a series LCR circuit, the inductive reactance is $$X_L = 2\pi f L = 2\pi \times 50 \times 0.5 \times 10^{-3} \approx 0.157 \,\Omega$$.

The capacitive reactance is $$X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi \times 50 \times 0.1 \times 10^{-12}} \approx 3.18 \times 10^{10} \,\Omega$$.

Since $$X_C \gg X_L$$, the net reactance is dominantly capacitive. The phase angle between the voltage and the current is given by $$\tan\phi = \frac{X_L - X_C}{R}$$. Here $$X_L - X_C \approx -3.18 \times 10^{10} \,\Omega$$ and $$R = 100 \,\Omega$$, so $$\tan\phi \approx -3.18 \times 10^8$$, giving $$\phi \approx -90^\circ$$. The negative sign means the current leads the voltage by $$\approx 90^\circ$$, which is characteristic of a predominantly capacitive circuit.

Therefore the phase angle between current and supplied voltage is $$\approx 90^\circ$$ and the circuit is predominantly capacitive.

Get AI Help

Video Solution

video

Create a FREE account and get:

  • Free JEE Mains Previous Papers PDF
  • Take JEE Mains paper tests

Free JEE Topicwise Questions

JEE Rotational MotionJEE Units & MeasurementsJEE Atomic StructureJEE GravitationJEE Periodic Table & PeriodicityJEE StatisticsJEE Inverse Trigonometric FunctionsJEE Magnetism & Magnetic MaterialsJEE Sequences & SeriesJEE MatricesJEE Alternating CurrentsJEE Carboxylic AcidsJEE Permutations & CombinationsJEE Work, Energy & PowerJEE Electromagnetic InductionJEE Electronic DevicesJEE d and f-Block ElementsJEE Chemical KineticsJEE Heat TransferJEE Three Dimensional GeometryJEE Magnetic Effects of CurrentJEE Hydrocarbons - AromaticJEE Electromagnetic WavesJEE Aldehydes & KetonesJEE Hydrocarbons - AlkanesJEE Applications of DerivativesJEE EquilibriumJEE Indefinite IntegrationJEE Chemical ThermodynamicsJEE ElectrochemistryJEE ProbabilityJEE BiomoleculesJEE Continuity & DifferentiabilityJEE Kinetic Theory of GasesJEE Vector AlgebraJEE Hydrocarbons - AlkynesJEE Differential EquationsJEE Current & ResistanceJEE Straight LinesJEE WavesJEE Redox ReactionsJEE Hydrocarbons - AlkenesJEE DeterminantsJEE SolutionsJEE Ray OpticsJEE Dual Nature of Matter & RadiationJEE Chemical Bonding & Molecular StructureJEE Complex NumbersJEE Sets, Relations & FunctionsJEE Electric Charges & FieldsJEE Laws of MotionJEE Fluid MechanicsJEE Basic Concepts in ChemistryJEE Trigonometric FunctionsJEE LimitsJEE Laws of ThermodynamicsJEE Kinematics - 2D MotionJEE p-Block Elements (Groups 13-18)JEE Simple Harmonic MotionJEE Electric Potential & CapacitanceJEE Coordination CompoundsJEE JEE 2D GeometryJEE CirclesJEE Definite IntegrationJEE EMF & Circuit AnalysisJEE Surface TensionJEE Atoms & NucleiJEE Laboratory Experiments - XIJEE Number SystemJEE Basic Principles of Organic ChemistryJEE Wave OpticsJEE Quadratic EquationsJEE Alcohols, Phenols & EthersJEE Organic Compounds with HalogensJEE DifferentiationJEE Conic SectionsJEE Nitrogen-Containing CompoundsJEE ElasticityJEE Practical Organic ChemistryJEE Kinematics - 1D MotionJEE Purification & CharacterisationJEE Binomial Theorem
Ask AI