A filament bulb \((500~\text{W},100~\text{V})\) is to be used in a \(230~\text{V}\) main supply. When a resistance\(R\) is connected in series, the bulb works perfectly and consumes \(500~\text{W}.\) The value of \(R\) is:
| 1. | \(230~\Omega\) | 2. | \(46~\Omega\) |
| 3. | \(26~\Omega\) | 4. | \(13~\Omega\) |
1. \(nB\)
2. \(n^2B\)
3. \(2nB\)
4. \(2n^2B\)
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by \(60^{\circ}\) is \(W\). Now the torque required to keep the magnet in this new position is:
1. \(\dfrac{W}{\sqrt{3}}\)
2. \(\sqrt{3}W\)
3. \(\dfrac{\sqrt{3}W}{2}\)
4. \(\dfrac{2W}{\sqrt{3}}\)
| 1. | \(1~\text{GHz}\) | 2. | \(100~\text{MHz}\) |
| 3. | \(62.8~\text{MHz}\) | 4. | \(6.28~\text{MHz}\) |
Which of the following combinations should be selected for better tuning of an \(LCR\) circuit used for communication?
1. \(R=20~\Omega ,~L=1.5~\text{H},~C=35~\mu \text{F}\)
2. \(R=25~\Omega ,~L=2.5~\text{H},~C=45~\mu \text{F}\)
3. \(R=15~\Omega ,~L=3.5~\text{H},~C=30~\mu \text{F}\)
4. \(R=25~\Omega ,~L=1.5~\text{H},~C=45~\mu \text{F}\)
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 \(2\) |
The potential differences across the resistance, capacitance, and inductance are \(80~\text{V}\), \(40~\text{V}\) and \(100~\text{V}\) respectively in an \(LCR\) circuit. The power factor of this circuit is:
1. \(0.4\)
2. \(0.5\)
3. \(0.8\)
4. \(1.0\)
A \(100~\Omega\) resistance and a capacitor of \(100~\Omega\) reactance are connected in series across a \(220~\text{V}\) source. When the capacitor is \(50\%\) charged, the peak value of the displacement current is:
1. \(2.2~\text{A}\)
2. \(11~\text{A}\)
3. \(4.4~\text{A}\)
4. \(11\sqrt{2}~\text{A}\)
Two identical glass \(\left(\mu_g = \frac{3}{2}\right )\) equiconvex lenses of focal length \(f\) each are kept in contact. The space between the two lenses is filled with water \(\left(\mu_w = \frac{4}{3}\right)\). The focal length of the combination is:
| 1. | \(\dfrac{f}{3}\) | 2. | \(f\) |
| 3. | \(\dfrac{4f}{3}\) | 4. | \(\dfrac{3f}{4}\) |
An air bubble in a glass slab with a refractive index \(1.5\) (near-normal incidence) is \(5~\text{cm}\) deep when viewed from one surface and \(3~\text{cm}\) deep when viewed from the opposite surface. The thickness (in \(\text{cm}\)) of the slab is:
| 1. | \(8\) | 2. | \(10\) |
| 3. | \(12\) | 4. | \(16\) |
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