An inductance of $\left(\frac{200}{\mathrm{\pi }}\right)\mathrm{mH}$, a capacitance of $\left(\frac{{10}^{-3}}{\mathrm{\pi }}\right)\mathrm{F}$ and a resistance of 10Ω are connected in series with an AC source 220 V, 50 Hz. The phase angle of the circuit is

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

A step-down transformer reduces the voltage of a transmission line from 2200 V to 220 V. The power delivered by it is 880 W and its efficiency is 88%. The input current is

• 4.65 mA

• 0.045 A

• 0.45 A

• 4.65 A

If emf E = 4 cos 1000t volt is applied to an L-R circuit of inductance 3 mH and resistance 4 Ω, the amplitude of the current in the circuit is

• $\frac{4}{\sqrt{7}}\mathrm{A}$

• 1.0 A

• $\frac{4}{7}\mathrm{A}$

• 0.8 A

A DC circuit contains 10Ω of resistance in series with 10 H coil. The impedance of the circuit is

• 10 Ω

• 20 Ω

• 1 Ω

• zero

In an L-R circuit, the current increases to three fourth of its maximum value in 4 s, then the time constant of the circuit is

• 2log_e 2

• $\frac{4}{{\log }_{\mathrm{e}} 2}$

• $\frac{2}{{\log }_{\mathrm{e}} 2}$

• $\frac{{\log }_{\mathrm{e}} 2}{2}$

In a circuit, the current lags behind the voltage by a phase difference of π/2, the circuit will contain which of the following?

• Only R

• Only C

• R and C

• Only L

In order to obtain time constant of 10 s in an RC circuit containing a resistance of 10³Ω, the capacity of the condenser should be :

• 10 μF

• 100 μF

• 1000 μF

• 10000 μF

178.

An a-particle, when accelerated through a potential difference of V volt, has a wavelength λ associated with it. In order to have the same λ, by what potential difference a proton must be accelerated?

• 8 V

• 6 V

• 4 V

• 12 V

The power factor of a series LCR circuit when at resonance is :

• zero

• 0.5

• 1.0

• Depends on values of L, C and R

For high frequency, capacitor offers :

• more resistance

• less resistance

• zero resistance

• none of these