Energy Stored in an Inductor

Q.

When the current coil changes from $5\mathrm{A}$ to $2\mathrm{A}$ in $0.1\mathrm{s}$, an average of $50\mathrm{V}$ is produced. The self-inductance of the coil is.

1. $6\mathrm{H}$

2. $0.67\mathrm{H}$

3. $1.67\mathrm{H}$

4. $3\mathrm{H}$

Q. A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be

1. Halved
2. The same
3. Doubled
4. Quadrupled

Q. A long cylindrical conductor of radius $R$ carries current $i$ as shown below. The current density $J$ is a function of radius $r$ as $J=br$ where $b$ is a constant. The magnetic field at a distance $r_1(r_1<R)$ is:

1. $\frac{{\mu }_{0}b{r}_1^2}{2}$
2. Zero
3. $\frac{{\mu }_{0}b{r}_1^3}{2}$
4. $\frac{{\mu }_{0}b{r}_1^2}{3}$

Q.

A coil of inductance L is carrying a steady current i. What is the nature of its stored energy?

1. Magnetic

2. Electrical

3. Both magnetic and electrical

4. Heat

Q. The current in a coil of self-inductance $2.0\text{H}$ is increasing according to equation $I=2\sin t^2\text{A}$. Find the amount of energy spent during the period when the current changes from $0$ to $2\text{A}$.

1. $2\text{J}$
2. $3\text{J}$
3. $4\text{J}$
4. $\text{None of these}$

Q. Energy stored in a coil of self – inductance 40mH carrying a steady current of 2 A is

1. 0.8 J
2. 8 J
3. 0.08 J
4. 80 J

Q. A $40$ $mH$ coil carries a current of $8A$, the energy stored in the coil is

1. $240$ $mJ$
2. $280$ $mJ$
3. $320$ $mJ$
4. $360$ $mJ$

Q.

In a uniform magnetic field B, a wire in the form of a semicircle of radius r rotates about the diameter of the circle with an angular frequency
$\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R, the mean power generated per period of rotation is

1. $\frac{\pi r^2\omega B}{2R}$

2. $\frac{(\pi r^2\omega B{)}^2}{8R}$

3. $\frac{(\pi r\omega B{)}^2}{2R}$

4. $\frac{(\pi r{\omega }^{2}B{)}^2}{8R}$

Q.

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

1. $637.5\text{J}$

2. $437.5\mathrm{J}$

3. $540\mathrm{J}$

4. $740\mathrm{J}$

Q. A square loop of side 20 cm is placed in a magnetic field $B=(5+2t^2)$; such that, the magnetic field is perpendicular to the plane of the loop. If resistance of loop is $2\Omega$, heat generated in 5 sec in joules is (write until two digits after the decimal point)

Q. A coil of resistance $20\Omega$ and inductance $5H$ has been connected to a $100V$ battery The energy stored in the coil after a long time is

1. $31.25J$
2. $62.5J$
3. $125J$
4. $250J$

Q. In the circuit shown in figure, $X$ is joined to $Y$ for a long time and then $X$ is joined to $Z$. The total heat produced in $R_2$ is

1. $\frac{L{E}^2}{2R_1^2}$
2. $\frac{L{E}^2}{2R_2^2}$
3. $\frac{L{E}^2}{2R_1{R}_2}$
4. $\frac{L{E}^2{R}_2}{2R_1^3}$

Q. If at $t=0$, switch $\text{S}$ is closed, at steady state find heat generated $\left(H\right)$ in the given circuit having a battery of $16\text{volts}$.

1. $640\mu \text{J}$
2. $192\mu \text{J}$
3. $1280\mu \text{J}$
4. $320\mu \text{J}$