Alternating Current

In a series resonant LCR circuit, the voltage across R is 100 volts and R = 1 kΩ with C = 2µF. The resonant frequency ω is 200 rad/s. At resonance the voltage across L is

• 4 × 10−3 V

• 2.5 × 10⁻² V

• 40 V

• 40 V

Two voltameters one of copper and another of silver, are joined in parallel. When a total charge q flows through the voltameters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are z₁ and z₂ respectively the charge which flows through the silver voltameter is

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

• 0.8

• 0.4

• 1.25

• 1.25

The phase difference between the alternating current and emf is π/2. Which of the following cannot be the constituent of the circuit?

• C alone

• R.L

• L.C

• L.C

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

• A.C. cannot pass through D.C.

• A.C. changes direction

• average value of current for complete cycle is zero

• average value of current for complete cycle is zero

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

• 50 V

• 50√2 V

• 100 V

• 100 V

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

• 4L

• 2L

• L/2

• L/2

For an RLC circuit driven with a voltage of amplitude v_m and frequency ${\omega }_0 = \frac{1}{\sqrt{LC}}$ the current exhibits resonance. The quality factor, Q is given by:

• $\frac{CR}{{\omega }_0}$

• $\frac{{\omega }_{0}L}{R}$

• $\frac{{\omega }_{0}R}{L}$

• $\frac{R}{\left({\omega }_{0}C\right)}$

An EM wave from air enters a medium. The electric fields are

${\overrightarrow{E}}_1 = E_{01} \hat{x} \cos \left[2\pi v\left(\frac{z}{c}-t\right)\right]$ in air and ${\overrightarrow{E}}_2 = E_{02} \hat{x} \cos [ k(2z-ct\left)\right]$ in medium, where the wave number k and frequency v refer to their values in air. The medium is non-magnetic. If ${\epsilon }_{r_1} and {\epsilon }_{r_2}$refer to relative permittivities of air and medium respectively, which of the following options is correct ?

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = \frac{1}{2}$

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = 4$

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = 2$

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = \frac{1}{4}$

If the rms value of sinusoidal input to a full wave rectifier is ${\mathrm{V}}_0/\sqrt{2}$, then the rms value of the rectifier's output is

• ${\mathrm{V}}_0/\sqrt{2}$

• ${{\mathrm{V}}_0}^2/\sqrt{2}$

• V₀²/2

• $\sqrt{2} {{\mathrm{V}}_0}^2$