JEE Alternating Currents PYQs with Video Solutions PDF, Download Now

In a series LCR circuit, a resistor of 300Ω, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____$$\times 10^{4}\text{ radians }s^{-1}$$

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:

An oscillating LC circuit consists of a 75 mH inductor and a 1.2 $$\mu$$F capacitor. If the maximum charge to the capacitor is 2.7 $$\mu$$C. The maximum current in the circuit will be ______ mA.

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

In an $$LCR$$ circuit shown in the following figure, what will be the readings of the voltmeter across the resistor and ammeter if an a.c. source of 220 V and 100 Hz is connected to it as shown?

For an RLC circuit driven with voltage of amplitude $$v_m$$ and frequency $$\omega_0 = \frac{1}{\sqrt{LC}}$$, the current exhibits resonance. The quality factor, Q is given by:

An alternating voltage source $$V = 260 \sin(628t)$$ is connected across a pure inductor of 5 mH. Inductive reactance in the circuit is:

A 750 Hz, 20 V(rms) source is connected to a resistance of 100 $$\Omega$$, an inductance of 0.1803 H and a capacitance of 10 $$\mu$$F all in series. The time in which the resistance (heat capacity 2 J/°C) will get heated by 10°C (assume no loss of heat to the surroundings) is close to:

A 100$$\Omega$$ resistance, a 0.1$$\mu$$F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

A capacitor of capacitance $$C = 80 \mu\text{F}$$ is completely charged to a potential difference of $$V_0 = 20 \text{ V}$$. It is then connected across an ideal inductor of inductance $$L = 2 \text{ mH}$$ to form an LC circuit. The circuit undergoes undamped electromagnetic oscillations. Find the magnitude of the maximum current (in Amperes) flowing through the circuit.

A series LCR circuit with $$L = \frac{100}{\pi}$$ mH, $$C = \frac{10^{-3}}{\pi}$$ F and $$R = 10$$ $$\Omega$$, is connected across an AC source of 220 V, 50 Hz supply. The power factor of the circuit would be _____.

a

If wattless current flows in the AC circuit, then the circuit is :

An AC source is connected to an inductance of $$100$$ mH, a capacitance of $$100$$ $$\mu$$F and a resistance of $$120$$ $$\Omega$$ as shown in figure. The time in which the resistance having a thermal capacity $$2$$ J °C$$^{-1}$$ will get heated by $$16°$$C is ______ s.

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 5O Hz nows through it. The ratio of inductive reactance to its resistance is_____.$$(\pi=3.14)$$

Given below are two statements :
Statement-I: The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.
Statement-II: In ac circuit, the average power delivered by the source never becomes zero.
In the light of the above statements, choose the correct answer from the options given below

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 $$\mu$$F is used in the resonant circuit. The self-inductance of coil necessary for resonance is $$x \times 10^{-8}$$ H. Find $$x$$.

In a series LCR circuit, an inductor of inductance $$L = 10 \,\, \text{mH}$$, a capacitor of capacitance $$C = 10 \,\, \mu\text{F}$$, and a resistor of resistance $$R = 10 \,\, \Omega$$ are connected to an AC source of voltage $$V = 220 \,\, \text{V}$$. At resonance, the power dissipated in the circuit is $$P \times 10^2 \,\, \text{W}$$. The integer value of $$P$$ is:

A LCR circuit behaves like a clamped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be:

A capacitor of capacitance $$100 \mu F$$ is charged to a potential of $$12$$ V and connected to a $$6.4$$ mH inductor to produce oscillations. The maximum current in the circuit would be :

A 0.07 H inductor and a 12 $$\Omega$$ resistor are connected in series to a 220 V, 50 Hz AC source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $$\pi$$ as $$\frac{22}{7}$$]

A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

A sinusoidal voltage $$V(t) = 210\sin 3000t$$ volt is applied to a series LCR circuit in which $$L = 10$$ mH, $$C = 25$$ $$\mu$$F and $$R = 100\Omega$$. The phase difference $$\Phi$$ between the applied voltage and resultant current will be

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

To light, a $$50 \text{ W}$$, $$100 \text{ V}$$ lamp is connected, in series with a capacitor of capacitance $$\dfrac{50}{\pi\sqrt{x}} \mu F$$, with $$200 \text{ V}$$, $$50 \text{ Hz}$$ AC source. The value of $$x$$ will be ______.

Given below are two statements:
Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs.
Statement II: Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.
In the light of the above statements, choose the correct answer from the options given below:

A series LCR circuit is subjected to an ac signal of $$200$$ V, $$50$$ Hz. If the voltage across the inductor $$(L = 10 \text{ mH})$$ is $$31.4$$ V, then the current in this circuit is :

An inductor of inductance $$2$$ $$\mu$$H is connected in series with a resistance, a variable capacitor and an AC source of frequency $$7$$ kHz. The value of capacitance for which maximum current is drawn into the circuit is $$\frac{1}{x}$$ F, where the value of $$x$$ is ______. (Take $$\pi = \frac{22}{7}$$)

In the above circuit, $$C = \frac{\sqrt{3}}{2}\mu F$$, $$R_2 = 20 \Omega$$, $$L = \frac{\sqrt{3}}{10} H$$ and $$R_1 = 10 \Omega$$. Current in $$L$$-$$R_1$$ path is $$I_1$$ and in C-$$R_2$$ path it is $$I_2$$. The voltage of AC source is given by, $$V = 200\sqrt{2} \sin(100t)$$ volts. The phase difference between $$I_1$$ and $$I_2$$ is:

A series LCR circuit is designed to resonate at an angular frequency $$\omega_0 = 10^5$$ rad s$$^{-1}$$. The circuit draws 16 W power from 120 V source at resonance. The value of resistance $$R$$ in the circuit is ______ $$\Omega$$.