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

• 2 log_e 2

• $\frac{4}{{\log }_{\mathrm{e}}2}$

• $\frac{2}{{\log }_{\mathrm{e}}2}$

• $\frac{{\log }_{\mathrm{e}}2}{2}$

Power factor of L-C-R circuit in resonation condition is

• 1

• $\frac{1}{2}$

• zero

• $\frac{1}{\sqrt{2}}$

An inductor and a capacitor are connected in an AC circuit inductance and capacitance are 1 H and 25 µF, then for maximum current, angular frequency will be (circuit is connected in series)

• 200 rad/s

• 50 rad/s

• 100 rad/s

• 150 rad/s

A step-up transformer has transformation ratio 3 : 2. The  voltage in the secondary coil, if the voltage in the primary is 30 V will be

• 300 V

• 90 V

• 45 V

• 23 V

In the inductive circuit given in the figure, the current rises after the switch is closed. At instant when the current is 15  mA, then potential difference across the inductor will be

• zero

• 240 V

• 180 V

• 60 V

The given circuit diagram shows a series L-C-R circuit connected to a variable frequency 230 V, source: L =5.0 H, C = 80 µF, R = 40 Ω

The frequency and impedance of the circuit at the resonating frequency are

• 50 rad/s and 5.75 A

• 1000 rad/s and 3 A

• 10 rad/s and 2 A

• 20 rad/s and 4 A

The instantaneous current and voltage of an AC circuit are given by I= 10 sin 300t A and V  = 200 sin 300t V. The power dissipation in the circuit is

• 500 W

• 2000 W

• 1000 W

• 100 W

In a series L-C-R circuit, the voltages across an inductor, a capacitor and a resistor are 30V, 30V and 60 V respectively. The phase difference between the applied voltage and the current in the circuit is

• O°

• 90°

• 30°

• 60°

An AC source, of voltage V =V_m sin ωt, is applied across a series RC circuit in which the capacitive impedance is 'a' times the resistance in the circuit. The value of the power factor of the circuit is

• O

• $1/\sqrt{1 + {\mathrm{a}}^2}$

• $\sqrt{1 + {\mathrm{a}}^2}$

• None of these

A step down transformer operated on a 2.5 kV line. It supplies a load with 20 A. The ratio of the primary winding to the secondary is 10 : 1. If the transformer is 90% efficient, the power output is

• 4.5 X 10⁴ W

• 4.5 × 10² W

• 6 x 10⁴ W

• 6 X 10⁴ w