A parallel plate air capacitor of capacitance \(C\) is connected to a cell of emf \(V\) and then disconnected from it. A dielectric slab of dielectric constant \(K,\) which can just fill the air gap of the capacitor is now inserted in it. Which of the following is incorrect?
| 1. | The potential difference between the plates decreases \(K\) times. |
| 2. | The energy stored in the capacitor decreases \(K\) times. |
| 3. | The change in energy stored is \(\frac{1}{2}CV^{2}\left ( \dfrac{1}{K} -1\right ) \) |
| 4. | The charge on the capacitor is not conserved. |
The electric field in a certain region is acting radially outward and is given by \(E=Aa.\) A charge contained in a sphere of radius \(a\) centered at the origin of the field will be given by:
| 1. | \(4 \pi \varepsilon_{{o}} {A}{a}^2\) | 2. | \(\varepsilon_{{o}} {A} {a}^2\) |
| 3. | \(4 \pi \varepsilon_{{o}} {A} {a}^3\) | 4. | \(\varepsilon_{{o}} {A}{a}^3\) |
A potentiometer wire has a length of \(4~\text{m}\) and resistance \(8~\Omega.\) The resistance that must be connected in series with the wire and an energy source of emf \(2~\text{V}\), so as to get a potential gradient of \(1~\text{mV}\) per cm on the wire is:
1. \(32~\Omega\)
2. \(40~\Omega\)
3. \(44~\Omega\)
4. \(48~\Omega\)
\({A, B}~\text{and}~{C}\) are voltmeters of resistance \(R,\) \(1.5R\) and \(3R\) respectively as shown in the figure above. When some potential difference is applied between \({X}\) and \({Y},\) the voltmeter readings are \({V}_{A},\) \({V}_{B}\) and \({V}_{C}\) respectively. Then:
| 1. | \({V}_{A} ={V}_{B}={V}_{C}\) | 2. | \({V}_{A} \neq{V}_{B}={V}_{C}\) |
| 3. | \({V}_{A} ={V}_{B}\neq{V}_{C}\) | 4. | \({V}_{A} \ne{V}_{B}\ne{V}_{C}\) |
| 1. | current density | 2. | current |
| 3. | drift velocity | 4. | electric field |
A wire carrying current \(I\) has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to \(X\)-axis while the semicircular portion of radius \(R\) is lying in the \(Y\text-Z\) plane. The magnetic field at point \(O\) is:
1. \(B=\frac{\mu i }{4\pi R}\left ( \pi \hat{i}+2\hat{k} \right )\)
2. \(B=-\frac{\mu i }{4\pi R}\left ( \pi \hat{i}-2\hat{k} \right )\)
3. \(B=-\frac{\mu i }{4\pi R}\left ( \pi \hat{i}+2\hat{k} \right )\)
4. \(B=\frac{\mu i }{4\pi R}\left ( \pi \hat{i}-2\hat{k} \right )\)
An electron moving in a circular orbit of radius \(r\) makes \(n\) rotations per second. The magnetic field produced at the centre has a magnitude:
| 1. | \(\dfrac{\mu_0ne}{2\pi r}\) | 2. | zero |
| 3. | \(\dfrac{n^2e}{r}\) | 4. | \(\dfrac{\mu_0ne}{2r}\) |
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. | \( \dfrac{1}{x^2} \) | 2. | \( \dfrac{1}{(2 x-a)^2} \) |
| 3. | \( \dfrac{1}{(2 x+a)^2} \) | 4. | \(\dfrac{1}{(2 x-a)(2 x+a)}\) |
A resistance \(R\) draws power \(P\) when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes \(Z\), the power drawn will be:
| 1. | \(P\Big({\large\frac{R}{Z}}\Big)^2\) | 2. | \(P\sqrt{\large\frac{R}{Z}}\) |
| 3. | \(P\Big({\large\frac{R}{Z}}\Big)\) | 4. | \(P\) |
Radiation of energy \(E\) falls normally on a perfectly reflecting surface. The momentum transferred to the surface is:
(\(c\) = velocity of light)
| 1. | \(E \over c\) | 2. | \(2E \over c\) |
| 3. | \(2E \over c^2\) | 4. | \(E \over c^2\) |
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