A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 μF and R = 100 Ω. The phase difference (Φ) between the applied voltage and resultant current will be:
- tan–1(0.17)
- tan–1(9.46)
- tan–1(0.30)
- tan–1(13.33)
The Correct Option is A
Solution and Explanation
The correct option is((A); tan–1(0.17).
XL = 3000 × 10 × 10–3 = 30Ω
\(X_c=\frac{1}{3000x25}×10^6=\frac{40}{3}Ω\)
So
\(X_L-X_C=30-\frac{40}{3}=\frac{50}{3}Ω\)
\(tanθ=\frac{X_L-X_C}{R}=\frac{50/3}{100}=\frac{1}{6}\)
So
\(θ=tan^{-1}(0.17)\)
Top Questions on LCR Circuit
Find output voltage in the given circuit.
- JEE Main - 2025
- Physics
- LCR Circuit
- In an LC circuit, the inductance \( L \) is 2 H and the capacitance \( C \) is 4 μF. What is the frequency of oscillation of the circuit?
- MHT CET - 2025
- Physics
- LCR Circuit
- A sinusoidal voltage produced by an AC generator at any instant \( t \) is given by an equation \( V = 311 \sin (314t) \). The rms value of voltage and frequency are respectively
- KCET - 2025
- Physics
- LCR Circuit
- The amplitude of the charge oscillating in a circuit decreases exponentially as $Q = Q_0 e^{-Rt/2L}$, where $Q_0$ is the charge at $t=0s$. The time at which charge amplitude decreases to 0.50 $Q_0$ is nearly:
[Given that $R = 15 \Omega$, $L = 12 mH$, $ln(2) = 0.693$]- NEET (UG) - 2024
- Physics
- LCR Circuit
- A series LCR circuit is subjected to an AC signal of 200 V, 50 Hz. If the voltage across the inductor (L = 10 mH) is 31.4 V, then the current in this circuit is ________ :
- JEE Main - 2024
- Physics
- LCR Circuit
Questions Asked in JEE Main exam
Nature of compounds TeO₂ and TeH₂ is___________ and ______________respectively.
- JEE Main - 2025
- Inorganic chemistry
- Let \( A = [a_{ij}] \) be a matrix of order 3 \(\times\) 3, with \(a_{ij} = (\sqrt{2})^{i+j}\). If the sum of all the elements in the third row of \( A^2 \) is \( \alpha + \beta\sqrt{2} \), where \(\alpha, \beta \in \mathbb{Z}\), then \(\alpha + \beta\) is equal to:
- JEE Main - 2025
- Matrices and Determinants
Consider the following sequence of reactions :
Molar mass of the product formed (A) is ______ g mol\(^{-1}\).- JEE Main - 2025
- Organic Chemistry
The magnitude of heat exchanged by a system for the given cyclic process ABC (as shown in the figure) is (in SI units):
- JEE Main - 2025
- Electric charges and fields
- The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:
- JEE Main - 2025
- Trigonometric Identities
Concepts Used:
LCR Circuit
An LCR circuit, also known as a resonant circuit, or an RLC circuit, is an electrical circuit consist of an inductor (L), capacitor (C) and resistor (R) connected in series or parallel.
Series LCR circuit
When a constant voltage source is connected across a resistor a current is induced in it. This current has a unique direction and flows from the negative to positive terminal. Magnitude of current remains constant.
Alternating current is the current if the direction of current through this resistor changes periodically. An AC generator or AC dynamo can be used as AC voltage source.
