Q. No.The current in a wire varies with time according to the equation \(I=(4+2t),\) where \(I\) is in ampere and \(t\) is in seconds. The quantity of charge which has passed through a cross-section of the wire during the time \(t=2\) s to \(t=6\) s will be:
| 1. | \(60\) C | 2. | \(24\) C |
| 3. | \(48\) C | 4. | \(30\) C |
| 1. | \(28\) C | 2. | \(30.5\) C |
| 3. | \(8\) C | 4. | \(82\) C |
2. \(-r\) and \(E\)
| 1. | \(1.5~\text{A}\) from \(\mathrm{B}\) to \(\mathrm{A}\) through \(E\) |
| 2. | \(0.2~\text{A}\) from \(\mathrm{B}\) to \(\mathrm{A}\) through \(E\) |
| 3. | \(0.5~\text{A}\) from \(\mathrm{A}\) to \(\mathrm{B}\) through \(E\) |
| 4. | \(\dfrac{5}{9}~\text{A}\) from \(\mathrm{A}\) to \(\mathrm{B}\) through \(E\) |
| 1. | \(1000\) | 2. | \(10\) |
| 3. | \(100\) | 4. | \(1\) |
The resistance of a wire is \(R\) ohm. If it is melted and stretched to \(n\) times its original length, its new resistance will be:
| 1. | \(nR\) | 2. | \(\frac{R}{n}\) |
| 3. | \(n^2R\) | 4. | \(\frac{R}{n^2}\) |
Two metal wires of identical dimensions are connected in series. If \(\sigma_1~\text{and}~\sigma_2\)
| 1. | \(\frac{2\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\) | 2. | \(\frac{\sigma_1 +\sigma_2}{2\sigma_1\sigma_2}\) |
| 3. | \(\frac{\sigma_1 +\sigma_2}{\sigma_1\sigma_2}\) | 4. | \(\frac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\) |
| 1. | current density | 2. | current |
| 3. | drift velocity | 4. | electric field |
A wire of resistance \(4~\Omega\) is stretched to twice its original length. The resistance of a stretched wire would be:
| 1. | \(4~\Omega\) | 2. | \(8~\Omega\) |
| 3. | \(16~\Omega\) | 4. | \(2~\Omega\) |
A ring is made of a wire having a resistance of \(R_0=12~\Omega.\). Find points \(\mathrm{A}\) and \(\mathrm{B}\), as shown in the figure, at which a current-carrying conductor should be connected so that the resistance \(R\) of the subcircuit between these points equals \(\frac{8}{3}~\Omega\)
| 1. | \(\dfrac{l_1}{l_2} = \dfrac{5}{8}\) | 2. | \(\dfrac{l_1}{l_2} = \dfrac{1}{3}\) |
| 3. | \(\dfrac{l_1}{l_2} = \dfrac{3}{8}\) | 4. | \(\dfrac{l_1}{l_2} = \dfrac{1}{2}\) |
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