Alternating Current

An ac circuit contains a resistance of \(1k\Omega\), a capacitor of \(0.1\mu F\) and an inductor of 1 mH connected in series. The resonance frequency of the circuit is approximately :

The amplitude of the charge oscillating in a circuit decreases exponentially as \(Q={Q}_{0}{e}^{-Rt/2L}\), where \({\mathrm{Q}}_{0}\) is the charge at \(t=0\mathrm{s}\). The time at which charge amplitude decreases to \(0.50{Q}_{0}\) is nearly :
[Given that \(\mathrm{R}=1.5\Omega ,\mathrm{L}=12\mathrm{mH},\ln (2)=0.693\) ]

[Re-NEET 2024]

The amplitude of the charge oscillating in a circuit decreases exponentially as \(Q={Q}_{0}{e}^{-Rt/2L}\), where \({\mathrm{Q}}_{0}\) is the charge at \(t=0\mathrm{s}\). The time at which charge amplitude decreases to \(0.50{Q}_{0}\) is nearly :
[Given that \(\mathrm{R}=1.5\Omega ,\mathrm{L}=12\mathrm{mH},\ln (2)=0.693\) ]

'In' an ideal transformer, the turns ratio is \(\frac{{N}_{p}}{{N}_{s}}=\frac{1}{2}\). The ratio \({V}_{s}:{V}_{p}\) is equal to (the symbols carry their usual meaning) :

[NEET 2024]

A step up transformer is connected to an ac mains supply of \(220\mathrm{V}\) to operate at \(11000\mathrm{V},88\) watt. The current in the secondary circuit, ignoring the power loss in the transformer, is :

[Re-NEET 2024]

The amplitude of the charge oscillating in a circuit decreases exponentially as \(Q={Q}_{0}{e}^{-Rt/2L}\), where \({\mathrm{Q}}_{0}\) is the charge at \(t=0\mathrm{s}\). The time at which charge amplitude decreases to \(0.50{Q}_{0}\) is nearly :
[Given that \(\mathrm{R}=1.5\Omega ,\mathrm{L}=12\mathrm{mH},\ln (2)=0.693\) ]

The amplitude of the charge oscillating in a circuit decreases exponentially as \(Q={Q}_{0}{e}^{-Rt/2L}\), where \({\mathrm{Q}}_{0}\) is the charge at \(t=0\mathrm{s}\). The time at which charge amplitude decreases to \(0.50{Q}_{0}\) is nearly :
[Given that \(\mathrm{R}=1.5\Omega ,\mathrm{L}=12\mathrm{mH},\ln (2)=0.693\) ]

The amplitude of the charge oscillating in a circuit decreases exponentially as \(Q={Q}_{0}{e}^{-Rt/2L}\), where \({\mathrm{Q}}_{0}\) is the charge at \(t=0\mathrm{s}\). The time at which charge amplitude decreases to \(0.50{Q}_{0}\) is nearly :
[Given that \(\mathrm{R}=1.5\Omega ,\mathrm{L}=12\mathrm{mH},\ln (2)=0.693\) ]

To an ac power supply of \(220\mathrm{V}\) at \(50\mathrm{Hz}\) , a resistor of \(20\Omega\), a capacitor of reactance \(25\Omega\) and an inductor of reactance \(45\Omega\) are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively -

[NEET 2025]

The peak value of an alternating current is 5 A and frequency is 60 Hz. How long will the current, starting from zero, take to reach the peak value?

To an ac power supply of \(220\mathrm{V}\) at \(50\mathrm{Hz}\) , a resistor of \(20\Omega\), a capacitor of reactance \(25\Omega\) and an inductor of reactance \(45\Omega\) are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively -

A step down transformer connected to an ac mains supply of \( 220 \mathrm{~V} \) is made to operate at \( 11 \mathrm{~V}, 44 \mathrm{~W} \) lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?

[NEET 2021]

In an ac circuit, an inductor, a capacitor and a resistor are connected in series with \({X}_{L}=R={X}_{C}\). Impedance of this circuit is:

[JEE Main 2021, 31 Aug (Shift 1)]

A series LCR circuit containing \( 5.0 \mathrm{H} \) inductor, \( 80 \mu \mathrm{F} \) capacitor and \( 40 \Omega \) resistor is connected to \( 230 \mathrm{~V} \) variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:-

[NEET 2021]

An AC current is given by \(I={I}_{1}\sin \omega t+{I}_{2}\cos \omega t\) . A hot wire ammeter will give a reading:

[JEE Main 2021, 17 Mar (Shift 1)]

In a series LCR circuit, the inductance L is \(10\mathrm{mH}\), capacitance C is \(1\mu \mathrm{F}\) and resistance R is \(100\Omega\). The frequency at which resonance occurs is :-

[NEET 2023]

A \( 40 \mu \mathrm{F} \) capacitor is connected to a \( 200 \mathrm{~V}, 50 \mathrm{~Hz} \) ac supply. The r.m.s value of the current in the circuit is, nearly

[NEET 2020]

A 12 V, 60 W lamp is connected to the secondary of a step down transformer, whose primary is connected to ac mains of 220 V. Assuming the transformer to be ideal, what is the current in the primary winding ?

[NEET 2023]

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

[JEE Main 2021, 26 Aug (Shift 1)]

\(\mathrm{A}10\Omega\) resistance is connected across \(220\mathrm{V}-50\mathrm{Hz}\mathrm{AC}\) supply. The time taken by the current to change from its maximum value to the rms value is:

A series LCR circuit is connected to an ac voltage source. When \( \mathrm{L} \) is removed from the circuit, the phase difference between current and voltage is \( \frac{\pi}{3} \). If instead \( C \) is removed from the circuit, the phase difference is again \( \frac{\pi}{3} \) between current and voltage. The power factor of the circuit is:-

[NEET 2020]

A \( 40 \mu \mathrm{F} \) capacitor is connected to a \( 200 \mathrm{~V}, 50 \mathrm{~Hz} \) ac supply. The r.m.s value of the current in the circuit is, nearly