**Question:**

A coil having $\mathrm{n}$ turns and resistance $R \Omega$ is connected with a galvanometer of resistance $4 R \Omega$. This combination is moved in time $t$ seconds from a magnetic field $W_{1}$ weber to $W_{2}$ weber. The induced current in the circuit is

Correct Option: 2

**Solution:**

### Related Questions

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer $G$ attached across the coil?

Three positions shown describe : (1) the magnet’s entry (2) magnet is completely inside and (3) magnet’s exit.

An elliptical loop having resistance $R$, of semi major axis $a$, and semi minor axis $b$ is placed in a magnetic field as shown in the figure. If the loop is rotated about the $x$-axis with angular frequency $\omega$, the average power loss in the loop due to Joule heating is :

A uniform magnetic field $B$ exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $4 \mathrm{~mm}$ and a total length of $30 \mathrm{~cm}$. The magnetic field changes with time at a steady rate $d B / d t=0.032 \mathrm{Ts}^{-1}$. The induced current in the loop is close to (Resistivity of the metal wire is $1.23 \times 10^{-8} \Omega \mathrm{m}$ )

At time $t=0$ magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next $5 \mathrm{~s}$, then induced EMF in the loop is:

Consider a circular coil of wire carrying constant current $I$, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by $\phi_{i}$.The magnetic flux through the area of the circular coil area is given by $\phi_{0}$. Which of the following option is correct?

A long solenoid of radius $R$ carries a time $(t)$ – dependent current $I(t)=I_{0} t(1-t)$. A ring of radius $2 R$ is placed coaxially near its middle. During the time interval $0 \leq t \leq 1$, the change as:

A planar loop of wire rotates in a uniform magnetic field. Initially, at $t=0$, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10 \mathrm{~s}$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

A very long solenoid of radius $R$ is carrying current $\mathrm{I}(\mathrm{t})=\mathrm{kte}^{-\alpha t}(k>0)$, as a function of time $(t \geq 0)$. Counter clockwise current is taken to be positive. A circular conducting coil of radius $2 R$ is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by:

Two coils ‘P’ and ‘Q’ are separated by some distance. When a current of 3 A flows through coil ‘ $\mathrm{P}$ ‘, a magnetic flux of $10^{-3} \mathrm{~Wb}$ passes through ‘ $\mathrm{Q}$ ‘. No current is passed through ‘ $Q$ ‘. When no current passes through ‘ $P$ ‘ and a current of $2 \mathrm{~A}$ passes through ‘ $\mathrm{Q}$ ‘, the flux through ‘ $\mathrm{P}$ ‘ is:

The self induced emf of a coil is 25 volts. When the current in it is changed at uniiform rate from 10 A to 25 $\mathrm{A}$ in $1 \mathrm{~s}$, the change in the energy of the inductance is: