Alternating Current

The magnetic flux through each turn of a coil having 200 turns is given as (t² $-$ 1) x 10^-3 Wb, where t is in second. The emf induced in the coil at t = 3s is

• 0.7 V

• 1.2 V

• 0.8 V

• 0.9 V

A beam of light travelling along X-axis is described by the electric field E_v = 600 $\frac{\mathrm{V}}{\mathrm{m}}$. sin$\mathrm{\omega } \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right)$, the maximum magnetic force on a charge q = 2e, moving along Y-axis with the speed of 3 × 10⁸ m/s is 

• 19.2 × 10^-17 N

• 1.92 × 10^-17

• 0.192

• None of these

An L-C-R series circuit with a resistance of 100 Ω is connected to 200 V (AC source) and angular frequency 300 rad/s. When only the capacitor is removed, then the current lags behind the voltage by 60°. When only the inductor is removed the current leads the voltage by 60°. The average power dissipated in original L-C-R circuit is

• 50 W

• 100 W

• 200 W

• 400 W

In an LCR circuit as shown in figure, both switches are open initially. Now switch S₁ is closed, S₂ kept open. (q is charge on the capacitor and τ = RC is capacitive time constant). Which of the following statement is correct?       

• At t = $\frac{\mathrm{\tau }}{2}$, q = CV ( 1 $-$ e^-1 )

• Work done by the battery is half of the energy dissipated in the resistor

• At t = τ, q = CV/2

• At t = τ, q = CV ( 1 $-$ e^-2 )

A circular coil of radius 10 cm, 500 turns and resistance 2 Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s. The
current induced in the coil is

(Horizontal component of the earth's magnetic field at that place is 3.0 x 10^-5 T)

• 1.9 × 10^-3 A

• 2.9 × 10^-3 A

• 3.9 × 10^-3 A

• 4.9 × 10^-3 A

A series resonant LCR circuit has a quality factor ( Q-factor) 0.4. If  R = 2 kΩ,  C = 0.1 μF, then the value of inductance is

• 0.1 H

• 0.064 H

• 2 H

• 5 H

Assertion:  At resonance, LCR series circuit have a minimum current. 

Reason:  At resonance, in LCR series circuit, the current  and  e.m.f are not in phase with each other.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

An inductive circuit contains a resistance of 10 Ω and an inductance of 2 H, If an AC voltage of 120 V and frequency 60 Hz is applied to this circuit, the current would be nearly

• 0.72 A

• 0.16 A

• 0.48 A

• 0.80 A

In an oscillating system, a restoring force is a must. In an L-C circuit, restoring force is provide by

• capacitor

• inductance

• resistance

• both (a) and (b)

In an AC circuit, voltage V = V₀sinωt  and inductor L is connected across the circuit. Then the instantaneous power will be

• $\frac{{\mathrm{V}}_0^2}{2\mathrm{\omega L}} \mathrm{sin\omega t}$

• $\frac{- {\mathrm{V}}_0^2}{2\mathrm{\omega L}} \mathrm{sin\omega t}$

• $\frac{- {\mathrm{V}}_0^2}{2\mathrm{\omega L}} \sin 2\mathrm{\omega t}$

• $\frac{{\mathrm{V}}_0^2}{\mathrm{\omega L}}\sin 2\mathrm{\omega t}$