Alternating Current

A fully charged capacitor $$C$$ with initial charge $${q_0}$$ is connected to a coil of self inductance $$L$$ at $$t=0.$$ The time at which the energy is stored equally between the electric and the magnetic fields is :

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 :

Match List I with List II. List I List II (a) Rectifier (i) Used either for stepping up or stepping down the a.c. voltage (b) Stabilizer (ii) Used to convert a.c. voltage into d.c. voltage (c) Transformer (iii) Used to remove any ripple in the rectified output voltage (d) Filter (iv) Used for constant output voltage even when the input voltage or load current change Choose the correct answer from the options given below :

An alternating current is given by the equation i = i₁ sin $$\omega$$t + i₂ cos $$\omega$$t. The rms current will be :

An AC current is given by I = I₁ sin$$\omega$$t + I₂ cos$$\omega$$t. A hot wire ammeter will give a reading :

The power factor of $$AC$$ circuit having resistance $$(R)$$ and inductance $$(L)$$ connected in series and an angular velocity $$\omega$$ is

In an $$LCR$$ series $$a.c.$$ circuit, the voltage across each of the components, $$L,C$$ and $$R$$ is $$50V$$. The voltage across the $$L.C$$ combination will be :

In a $$LCR$$ circuit capacitance is changed from $$C$$ to $$2$$ $$C$$. For the resonant frequency to remain unchaged, the inductance should be changed from $$L$$ to

Alternating current can not be measured by $$D.C.$$ ammeter because

The self inductance of the motor of an electric fan is $$10$$ $$H$$. In order to impart maximum power at $$50$$ $$Hz$$, it should be connected to a capacitance of

A circuit has a resistance of $$12$$ $$ohm$$ and an impedance of $$15$$ $$ohm$$. The power factor of the circuit will be

The phase difference between the alternating current and $$emf$$ is $${\pi \over 2}.$$ Which of the following cannot be the constituent of the circuit?

In a series resonant $$LCR$$ circuit, the voltage across $$R$$ is $$100$$ volts and $$R = 1\,k\Omega$$ with $$C = 2\mu F.$$ The resonant frequency $$\omega$$ is $$200$$ $$rad/s$$. At resonance the voltage across $$L$$ is

In an $$a.c.$$ circuit the voltage applied is $$E = {E_0}\,\sin \,\omega t.$$ The resulting current in the circuit is $$I = {I_0}\sin \left( {\omega t - {\pi \over 2}} \right).$$ The power consumption in the circuit is given by

A resistance of 40 $$\Omega$$ is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to the rms value :

A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that R=5 $$\Omega$$, L=25 mH and C=1000 $$\mu$$F. The total impedance, and phase difference between the voltage across the source and the current will respectively be :

In an a.c. circuit, the instantaneous e.m.f. and current are given by e = 100 sin 30 t i = 20 sin $$\left( {30t - {\pi \over 4}} \right)$$ In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively

An ideal capacitor of capacitance $$0.2\,\mu F$$ is charged to a potential difference of $$10$$ $$V.$$ The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $$0.5$$ $$mH.$$ The current at a time when the potential difference across the capacitor is $$5$$ $$V,$$ is :

A circuit connected to an ac source of emf e = e₀sin(100t) with t in seconds, gives a phase difference of $$\pi$$/4 between the emf e and current i. Which of the following circuits will exhibit this ?