Q. No.The magnetic potential energy stored in a certain inductor is \(25\) mJ, when the current in the inductor is \(60\) mA. This inductor is of inductance:
1. \(0.138\) H
2. \(138.88\) H
3. \(1.389\) H
4. \(13.89\) H
1. \(0.138\) H
2. \(138.88\) H
3. \(1.389\) H
4. \(13.89\) H
A long solenoid of diameter \(0.1\) m has \(2 \times 10^4\) turns per meter. At the center of the solenoid, a coil of \(100\) turns and radius \(0.01\) m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to \(0\) A from \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\) then the total charge flowing through the coil during this time is:
1. \(16~\mu \text{C}\)
2. \(32~\mu \text{C}\)
3. \(16\pi~\mu \text{C}\)
4. \(32\pi~\mu \text{C}\)
A uniform magnetic field is restricted within a region of radius \(r\). The magnetic field changes with time at a rate \(\frac{dB}{dt}\). Loop \(1\) of radius \(R>r\) is enclosed within the region \(r\) and loop \(2\) of radius \(R\) is outside the region of the magnetic field as shown in the figure. Then, the emf generated is:
| 1. | zero in loop \(1\) and zero in loop \(2\) |
| 2. | \(-\frac{dB}{dt}\pi r^2\) in loop \(1\) and zero in loop \(2\) |
| 3. | \(-\frac{dB}{dt}\pi R^2\) in loop \(1\) and zero in loop \(2\) |
| 4. | zero in loop \(1\) and not defined in loop \(2\) |
An electron moves on a straight-line path \(XY\) as shown. The \(\mathrm{abcd}\) is a coil adjacent to the path of electrons. What will be the direction of current if any, induced in the coil?
| 1. | \(\mathrm{abcd}\) |
| 2. | \(\mathrm{adcb}\) |
| 3. | The current will reverse its direction as the electron goes past the coil |
| 4. | No current included |
A conducting square frame of side \(a\) and a long straight wire carrying current \(I\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v.\) The emf induced in the frame will be proportional to:
1. \( \frac{1}{x^2} \)
2. \( \frac{1}{(2 x-a)^2} \)
3. \( \frac{1}{(2 x+a)^2} \)
4. \(\frac{1}{(2 x-a)(2 x+a)}\)
A thin semicircular conducting the ring \((PQR)\) of radius \(r\) is falling with its plane vertical in a horizontal magnetic field \(B,\) as shown in the figure. The potential difference developed across the ring when it moves with speed \(v\) is:
| 1. | zero |
| 2. | \(Bv\pi r^{2}/2\) and \(P\) is at a higher potential |
| 3. | \(\pi rvB\) and \(R\) is at a higher potential |
| 4. | \(2BvR\) and \(R\) is at higher potential |
A coil of self-inductance \(L\) is connected in series with a bulb \(\mathrm{B}\) and an AC source. The brightness of the bulb decreases when:
| 1. | number of turns in the coil is reduced. |
| 2. | a capacitance of reactance \(X_C = X_L\) is included in the same circuit. |
| 3. | an iron rod is inserted in the coil. |
| 4. | frequency of the AC source is decreased. |
| 1. | twice per revolution. |
| 2. | four times per revolution. |
| 3. | six times per revolution. |
| 4. | once per revolution. |
A coil of resistance \(400~\Omega\) is placed in a magnetic field. The magnetic flux \(\phi~\text{(Wb)}\) linked with the coil varies with time \(t~\text{(s)}\) as \(\phi=50t^{2}+4.\) The current in the coil at \(t=2~\text{s}\) is:
1. \(0.5~\text{A}\)
2. \(0.1~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)
© 2024 GoodEd Technologies Pvt. Ltd.