JEE Main - 11th April 2015

An alternating voltage source $V=260\sin \left(628t\right)$ is connected across a pure inductor of $5 \mathrm{mH}$. Inductive reactance in the circuit is:

For the given circuit, in the steady state, $\left|V_B-V_D\right|=$ _____ $\mathrm{V}$.

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed:

A. By changing the magnitude of the magnetic field within the coil.

B. By changing the area of coil within the magnetic field.

C. By changing the angle between the direction of magnetic field and the plane of the coil.

D. By reversing the magnetic field direction abruptly without changing its magnitude.

Choose the most appropriate answer from the options given below:

An inductor of $0.5 \mathrm{mH}$, a capacitor of $20 \mathrm{\mu F}$ and resistance of $20 \mathrm{\Omega }$ are connected in series with a $220 \mathrm{V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x} \mathrm{A}$. The value of $x$ is-

A series LCR circuit consists of $R=80 \Omega$. $X_L=100 \Omega$, and $X_C=40 \Omega$. The input voltage is $2500 \cos \left(100\pi t\right) \mathrm{V}$. The amplitude of current, in the circuit, is _____  $\mathrm{A}$.

Match the List-I with List-II.

Choose the correct answer from the options given below:

A series LCR circuit is connected to an ac source of $220 \mathrm{V}, 50 \mathrm{Hz}$. The circuit contain a resistance $R=100 \mathrm{\Omega }$ and an inductor of inductive reactance $X_L=79.6 \mathrm{\Omega }$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ______ $\mathrm{\mu F}$.

A square shaped coil of area $70 {\mathrm{cm}}^2$ having $600$ turns rotates in a magnetic field of $0.4 \mathrm{Wb} {\mathrm{m}}^{–2}$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes $500$ revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $60°$ with the field, will be ______ $\mathrm{V}$.

(Take $\pi \mathit{=}\frac{\mathit{22}}{\mathit{7}}$)