Question

A $\mathrm{L}\mathrm{C}\mathrm{R}$ circuit behaves like a clamped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant $\text{'}{b}^{\text{'}},$ the correct equivalence would be:

JEE Main 2020 (07 Jan Shift 1)

Options

• A: $L\leftrightarrow m,C\leftrightarrow k,R\leftrightarrow b$
• B: $L\leftrightarrow \frac{1}{b},C\leftrightarrow \frac{1}{m},R\leftrightarrow \frac{1}{k}$
• C: $L\leftrightarrow k,C\leftrightarrow b,R\leftrightarrow m$
• D: $L\leftrightarrow m,C\leftrightarrow \frac{1}{k},R\leftrightarrow b$

Question

In a circuit consisting of a capacitance and a generator with alternating emf, $E_g=E_{go}sin\omega t, V_C$ and $I_{\mathit{C}}$ are the voltage and current. Correct phasor diagram for such circuit is

JEE Main 2021 (22 Jul Shift 1)

Options

• A:
• B:
• C:
• D:

Question

Match List-I with List-II.

Choose the correct answer from the options given below.

JEE Main 2021 (22 Jul Shift 1)

Options

• A: (a) - (ii) ; (b) - (i) ; (c) - (iv) ; (d) - (iii)
• B: (a) - (ii) ; (b) - (i) ; (c) - (iii) ; (d) - (iv)
• C: (a) - (iii) ; (b) - (i) ; (c) - (iv); (d) - (ii)
• D: (a) - (iv) ; (b) - (iii) ; (c) - (ii); (d) - (i)

Question

A series LCR circuit driven by $300 \mathrm{V}$ at a frequency of $50 \mathrm{Hz}$ contains a resistance $\mathrm{R}=3 \mathrm{k\Omega }$, an inductor of inductive reactance ${\mathrm{X}}_{\mathrm{L}}=250\pi \mathrm{\Omega }$ and an unknown capacitor. The value of capacitance to maximise the average power should be:
$\left(\text{take} {\pi }^2=10\right)$

JEE Main 2021 (26 Aug Shift 1)

Options

• A: $400 \mathrm{\mu F}$
• B: $4 \mu \mathrm{F}$
• C: $40 \mu \mathrm{F}$
• D: $25 \mu \mathrm{F}$

Question

Match List - I with List - II.

JEE Main 2022 (25 Jun Shift 1)

Options

• A: $\left(\mathrm{A}\right)-\left(\mathrm{II}\right),\left(\mathrm{B}\right)-\left(\mathrm{I}\right),\left(\mathrm{C}\right)-\left(\mathrm{IV}\right),\left(\mathrm{D}\right)-\left(\mathrm{III}\right)$
• B: $\left(\mathrm{A}\right)-\left(\mathrm{II}\right),\left(\mathrm{B}\right)-\left(\mathrm{I}\right),\left(\mathrm{C}\right)-\left(\mathrm{III}\right),\left(\mathrm{D}\right)-\left(\mathrm{IV}\right)$
• C: $\left(\mathrm{A}\right)-\left(\mathrm{III}\right),\left(\mathrm{B}\right)-\left(\mathrm{IV}\right),\left(\mathrm{C}\right)-\left(\mathrm{II}\right),\left(\mathrm{D}\right)-\left(\mathrm{I}\right)$
• D: $\left(\mathrm{A}\right)-\left(\mathrm{III}\right),\left(\mathrm{B}\right)-\left(\mathrm{I}\right),\left(\mathrm{C}\right)-\left(\mathrm{II}\right),\left(\mathrm{D}\right)-\left(\mathrm{IV}\right)$

Question

A series LCR circuit has $L=0.01 \mathrm{H},R=10 \mathrm{\Omega }$ and $C=1 \mu \mathrm{F}$ and it is connected to ac voltage of amplitude $\left(V_m\right) 50 \mathrm{V}$. At frequency $60\%$ lower than resonant frequency, the amplitude of current will be approximately

JEE Main 2022 (27 Jul Shift 2)

Options

• A: $466 \mathrm{mA}$
• B: $312 \mathrm{mA}$
• C: $238 \mathrm{mA}$
• D: $196 \mathrm{mA}$

Question

For a series $LCR$ circuit, $I$ vs $\omega$ curve is shown 

(a) To the left of ${\omega }_r$, the circuit is mainly capacitive.
(b) To the left of ${\omega }_r$, the circuit is mainly inductive.
(c) At ${\omega }_r$, impedance of the circuit is equal to the resistance of the circuit.
(d) At ${\omega }_r$, impedance of the circuit is $0$.

Choose the most appropriate answer from the options given below.

JEE Main 2022 (29 Jun Shift 1)

Options

• A: (a) and (d) only
• B: (b) and (d) only
• C: (a) and (c) only
• D: (b) and (c) only

Question

A telegraph line of length $100 \mathrm{km}$ has a capacity of $0.01 \mu \mathrm{F} {\mathrm{km}}^{-1}$ and it carries an alternating current at $0.5$ kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is _____ $\mathrm{mH}$. (If $\pi =\sqrt{10}$)

JEE Main 2022 (28 Jun Shift 1)

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Question

In a series $LR$ circuit with $X_L=R$, power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C=X_L$ is added to the circuit the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be :

JEE Main 2023 (30 Jan Shift 1)

Options

• A: $1:3$
• B: $1:\sqrt{2}$
• C: $1:1$
• D: $1:2$

Question

A series LCR circuit is connected to an ac source of $220 \mathrm{V}, 50 \mathrm{Hz}$. The circuit contain a resistance $R=100 \mathrm{\Omega }$ and an inductor of inductive reactance $X_L=79.6 \mathrm{\Omega }$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ______ $\mathrm{\mu F}$.

JEE Main 2023 (01 Feb Shift 1)

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Question

When a $d c$ voltage of $100 \mathrm{~V}$ is applied to an inductor, a $d c$ current of $5 \mathrm{~A}$ flows through it. When an ac voltage of $200 \mathrm{~V}$ peak value is connected to inductor, its inductive reactance is found to be $20 \sqrt{3} \Omega$. The power dissipated in the circuit is _______ W.

JEE Main 2024 (06 Apr Shift 1)

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Question

A coil of negligible resistance is connected in series with $90 \Omega$ resistor across $120 \mathrm{~V}, 60 \mathrm{~Hz}$ supply. A voltmeter reads $36 \mathrm{~V}$ across resistance. Inductance of the coil is :

JEE Main 2024 (08 Apr Shift 2)

Options

• A: $0.286 \mathrm{H}$
• B: $0.76 \mathrm{H}$
• C: $2.86 \mathrm{H}$
• D: $0.91 \mathrm{H}$

Question

An alternating emf $\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}$ volt is applied to a capacitor of $2 \mu \mathrm{F}$, the rms value of current in the circuit is _____$\mathrm{mA}$,

JEE Main 2024 (08 Apr Shift 2)

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Question

A capacitor of reactance $4 \sqrt{3} \Omega$ and a resistor of resistance $4 \Omega$ are connected in series with an ac source of peak value $8 \sqrt{2} \mathrm{~V}$. The power dissipation in the circuit is ________ W.

JEE Main 2024 (09 Apr Shift 2)

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Question

In the given figure, the charge stored in $6\mu \mathrm{F}$ capacitor, when points $A$ and $B$ are joined by a connecting wire is _______$\mu \mathrm{C}$.

JEE Main 2024 (29 Jan Shift 2)

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Question

The primary side of a transformer is connected to $230 \mathrm{V}, 50 \mathrm{Hz}$ supply. The turn ratio of primary to secondary winding is $10 : 1$. Load resistance connected to the secondary side is $46 \mathrm{\Omega }$. The power consumed in it is:

JEE Main 2024 (27 Jan Shift 2)

Options

• A: $12.5 \mathrm{W}$
• B: $10.0 \mathrm{W}$
• C: $11.5 \mathrm{W}$
• D: $12.0 \mathrm{W}$