Q. No.The resistance of a wire is \(R~\Omega\). If it is melted and stretched \(n\) times its original length, its new resistance will be:
1. \(\frac{R}{n}\)
2. \(n^{2}R\)
3. \(\frac{R}{n^{2}}\)
4. \(nR\)
1. \(\frac{R}{n}\)
2. \(n^{2}R\)
3. \(\frac{R}{n^{2}}\)
4. \(nR\)
A carbon resistor (47 ± 4.7) kΩ is to be marked with rings of different colours for its identification. The colour code sequence will be:
1. Violet - Yellow - Orange - Silver
2. Yellow - Violet - Orange - Silver
3. Yellow - Green - Violet - Gold
4. Green - Orange - Violet - Gold
The figure shows a circuit that contains three identical resistors with resistance \(R = 9.0~\Omega\) each, two identical inductors with inductance \(L = 2.0~\text{mH}\) each, and an ideal battery with emf \(\varepsilon = 18~\text{V}\). The current \('i'\) through the battery just after the switch is closed will be:
1. \(0.2~\text{A}\)
2. \(2~\text{A}\)
3. \(4~\text{A}\)
4. \(2~\text{mA}\)
The potential difference \(V_\mathrm{A}-V_\mathrm{B}\) between the points \(\mathrm{A}\) and \(\mathrm{B}\) in the given figure is:
| 1. | \(-3~\text{V}\) | 2. | \(+3~\text{V}\) |
| 3. | \(+6~\text{V}\) | 4. | \(+9~\text{V}\) |
A filament bulb (\(500\) W, \(100\) V) is to be used in a \(230\) V main supply. When a resistance\(R\) is connected in series, the bulb works perfectly and consumes \(500\) W. The value of \(R\) is:
| 1. | \(230\) | 2. | \(46\) |
| 3. | \(26\) | 4. | \(13\) |
| 1. | \(\dfrac{a^3R}{3b}\) | 2. | \(\dfrac{a^3R}{2b}\) |
| 3. | \(\dfrac{a^3R}{b}\) | 4. | \(\dfrac{a^3R}{6b}\) |
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. | \(\frac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\) |
\(\mathrm{A, B}~\text{and}~\mathrm{C}\) are voltmeters of resistance \(R\), \(1.5R\) and \(3R\) respectively as shown in the figure above. When some potential difference is applied between \(\mathrm{X}\) and \(\mathrm{Y}\), the voltmeter readings are \({V}_\mathrm{A}\), \({V}_\mathrm{B}\) and \({V}_\mathrm{C}\) respectively. Then:
| 1. | \({V}_\mathrm{A} ={V}_\mathrm{B}={V}_\mathrm{C}\) | 2. | \({V}_\mathrm{A} \neq{V}_\text{B}={V}_\mathrm{C}\) |
| 3. | \({V}_\mathrm{A} ={V}_\mathrm{B}\neq{V}_\mathrm{C}\) | 4. | \({V}_\mathrm{A} \ne{V}_\mathrm{B}\ne{V}_\mathrm{C}\) |
| 1. | current density | 2. | current |
| 3. | drift velocity | 4. | electric field |
The figure given below shows a circuit when resistances in the two arms of the meter bridge are \(5~\Omega\) and \(R\), respectively. When the resistance \(R\) is shunted with equal resistance, the new balance point is at \(1.6l_1\). The resistance \(R\) is:
1. \(10~\Omega\)
2. \(15~\Omega\)
3. \(20~\Omega\)
4. \(25~\Omega\)
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