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Primary side of a transformer is connected to \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) supply. Turns ratio of primary to secondary winding is \( 10:1 \). Load resistance connected to secondary side is \( 46 \, \Omega \). The power consumed in it is:

In the given electromagnetic wave \( E_{y} = 600 \, \sin(\omega t - kx) \, \text{V m}^{-1} \), intensity of the associated light beam is
(in \( \frac{W}{m^{2}} \) : Given \( \epsilon_{0} = 9 \times 10^{-12} \, \text{C}^{2} \, \text{N}^{-1} \, \text{m}^{-2} \))

If frequency of electromagnetic wave is \( 60 \, \text{MHz} \) and it travels in air along \( z \) direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in \( \text{m} \)) is:

In an a.c. circuit, voltage and current are given by: \( V = 100 \sin(100 t) \, \text{V} \) and \( I = 100 \sin(100 t + \dfrac{\pi}{3}) \, \text{mA} \) respectively. The average power dissipated in one cycle is:

A series LCR circuit with \(\displaystyle L = \frac{100}{\pi} \, \text{mH} \), \(\displaystyle C = \frac{10^{-3}}{\pi} \, \text{F} \) and \( R = 10 \, \Omega \), is connected across an ac source of \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) supply. The power factor of the circuit would be __________ .

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of \( 20 \, \mu \text{F} \) is __________ \( \text{V} \).

An AC voltage \( V = 20 \sin 200\pi t \) is applied to a series LCR circuit which drives a current \( I = 10 \sin\left(200\pi t + \dfrac{\pi}{3}\right) \). The average power dissipated is:

Primary coil of a transformer is connected to \( 220 \, \text{V} \) a.c. Primary and secondary turns of the transforms are \( 100 \) and \( 10 \) respectively. Secondary coil of transformer is connected to two series resistances shown in figure. The output voltage \( (V_0) \) is:

A series L.R circuit connected with an ac source \( E = (25 \sin 1000 t) \, \text{V} \) has a power factor of \( \frac{1}{\sqrt{2}} \). If the source of emf is changed to \( E = (20 \sin 2000 t) \, \text{V} \), the new power factor of the circuit will be:

10.

A capacitor reactance \( 4\sqrt{3} \, \Omega \) and a resistor of resistance \( 4 \, \Omega \) are connected in series with an ac source of peak value \( 8\sqrt{2} \, V \). The power dissipation in the circuit is ......\( W \).

11.

Given below are two statements:
Statement I: In an LCR series circuit, current is maximum at resonance.
Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.
In the light of the above statements, choose the correct from the options given below:

12.

Match List I with List II.

Choose the correct answer from the options given below:

13.

A series LCR circuit is subjected to an ac signal of \( 200\,\text{V} \), \( 50\,\text{Hz} \). If the voltage across the inductor (\( L = 10\,\text{mH} \)) is \( 31.4\,\text{V} \), then the current in this circuit is ________.

14.

The magnetic field in a plane electromagnetic wave is \( B_{y} = (3.5 \times 10^{-7}) \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) \, \text{T} \). The corresponding electric field will be

15.

A \( \text{LCR} \) circuit is at resonance for a capacitor \( C \), inductance \( L \) and resistance \( R \). Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

16.

An alternating emf \( E = 110\sqrt{2} \, \sin100 t \) volt is applied to a capacitor of \( 2\,\mu \text{F} \), the rms value of current in the circuit is ______ \( \text{mA} \).

17.

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is \( 2.5\,\text{nF} \). If resistance of \( 200\,\Omega \) and \( 100\,\text{mH} \) inductor is being used in the given circuit. The frequency of ac source is ______ \( \times 10^{3} \) \( \text{Hz} \). (given \( \pi^{2}=10 \) )

18.

A coil of negligible resistance is connected in series with \( 90 \, \Omega \) resistor across \( 120 \, \text{V} \), \( 60 \, \text{Hz} \) supply. A voltmeter reads \( 36 \, \text{V} \) across resistance. Inductance of the coil is:

19.

When a dc voltage of \( 100\,\text{V} \) is applied to an inductor a dc current of \( 5\,\text{A} \) flows through it. When an ac voltage of \( 200\,\text{V} \) peak value is connected to inductor, its inductive reactance is found to be \( 20\sqrt{3}\,\Omega \). The power dissipated in the circuit is ________ \( \text{W} \).

20.

A power transmission line feeds input power at \( 2.3\,\text{kV} \) to a step down transformer with its primary winding having \( 3000 \) turns. The output power is delivered at \( 230\,\text{V} \) by the transformer. The current in the primary of the transformer is \( 5\,\text{A} \) and it efficiency is \( 90\% \). The winding of transformer is made of copper. The output current of transformer is ______ \( \text{A} \).

21.

Match List-I with List-II:

List-I EM- Wave	List-II Wavelength Range
(A) Infra-red	(I) \( < 10^{-3} \, \text{nm} \)
(B) Ultraviolet	(II) \( 400 \, \text{nm} \) to \( 1 \, \text{nm} \)
(C) X-rays	(III) \( 1 \, \text{nm} \) to \( 700 \, \text{nm} \)
(D) Gamma rays	(IV) \( 1 \, \text{nm} \) to \( 10^{-3} \, \text{nm} \)

Choose the correct answer from the options given below:

22.

In series LCR circuit, the capacitance is changed from \( C \) to \( 4C \). To keep the resonance frequency unchanged, the new inductance should be:

23.

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to:
A. Pure inductor.
B. Pure capacitor.
C. Pure resistor.
D. Combination of an inductor and capacitor.
Choose the correct answer from the options given below:

24.

Electromagnetic waves travel in a medium with speed of \( 1.5 \times 10^{8} \, \text{m s}^{-1} \). The relative permeability of the medium is \( 2.0 \). The relative permittivity will be:

25.

A alternating current at any instant is given by \( i = \left[ 6 + \sqrt{56}\,\sin\!\left(100\pi t + \frac{\pi}{3}\right) \right] \,\text{A} \). The rms value of the current is _______ \( \text{A} \).

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