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Temperature dependence of resistivity $\mathrm{}$\(\rho(T)\) of semiconductors, insulators, and metals is significantly based on the following factors:

(a) | number of charge carriers can change with temperature \(T\). |

(b) | the time interval between two successive collisions can depend on \(T\). |

(c) | length of material can be a function of \(T\). |

(d) | mass of carriers is a function of \(T\). |

Which of the above statements is correct?

1. | (a, b) | 2. | (c, d) |

3. | (b, c) | 4. | (b, d) |

Subtopic: Derivation of Ohm's Law |

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The measurement of an unknown resistance \(R\) is to be carried out using a Wheatstone bridge. Two students perform an experiment in two ways. The first students take \(R_2=10~\Omega\) and \(R_1=5~\Omega\). The other student takes \(R_2=1000~\Omega\) ${\mathrm{}}_{}$and \(R_1=500~\Omega\). In the standard arm, both take \(R_3=5~\Omega\).

Both find \(R = \dfrac{R_{2}}{R_{1}} R_{3} = 10 ~ \Omega \) within errors.

(a) | The errors of measurement of the two students are the same. |

(b) | Errors of measurement do depend on the accuracy with which \(R_2\) and \(R_1\) can be measured. |

(c) | If the student uses large values of \(R_2\) and \(R_1\), the currents through the arms will be feeble. This will make the determination of the null point accurately more difficult. |

(d) | Wheatstone bridge is a very accurate instrument and has no errors of measurement. |

Choose the correct option:

1. (a, c)

2. (c, d)

3. (b, c)

4. (c, d)

Subtopic: Wheatstone Bridge |

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In a meter bridge, point D is a neutral point as shown in the figure.

a. | The meter bridge can have no other neutral point for this set of resistances. |

b. | When the jockey contacts a point on the meter wire left of D, current flows to B from the wire. |

c. | When the jockey contacts a point on the meter wire to the right of D, current flows from B to the wire through the galvanometer. |

d. | When R is increased, the neutral point shifts to left. |

Which of the above statements is correct?

1. (a, c)

2. (a, d)

3. (b, c)

4. (c, d)

Subtopic: Meter Bridge & Potentiometer |

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Consider a current carrying wire (current \(\text{I}\)) in the shape of a circle. Note that as the current progresses along the wire, the direction of \(\text{j}\) (current density) changes in an exact manner, while the current \(\text{I}\) remains unaffected. The agent that is essentially responsible for it is:

1. | source of emf. |

2. | the electric field produced by charges accumulated on the surface of the wire. |

3. | the charges just behind a given segment of wire which push them just the right way by repulsion. |

4. | the charges ahead. |

Subtopic: Current & Current Density |

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Two batteries of emf ${\epsilon}_{1}\text{and}{\epsilon}_{2}({\epsilon}_{2}{\epsilon}_{1})$ and internal resistances ${\mathrm{r}}_{1}\mathrm{and}{\mathrm{r}}_{2}$ respectively are connected in parallel as shown in the figure.

1. | The equivalent emf ${\mathrm{\epsilon}}_{\mathrm{eq}}$ of the two cells is between ${\epsilon}_{1}\text{and}{\epsilon}_{2}.\text{i.e,}{\epsilon}_{1}{\epsilon}_{eq}{\epsilon}_{2}$ |

2. | The equivalent emf ${\mathrm{\epsilon}}_{\mathrm{eq}}$ is smaller than ${\mathrm{\epsilon}}_{1}$ |

3. | The ${\mathrm{\epsilon}}_{\mathrm{eq}}$ is given by ${\epsilon}_{eq}={\epsilon}_{1}+{\epsilon}_{2}$ always |

4. | ${\mathrm{\epsilon}}_{\mathrm{eq}}$ is independent of internal resistances ${\mathrm{r}}_{1}\mathrm{and}{\mathrm{r}}_{2}$ |

Subtopic: Grouping of Cells |

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A resistance R is to be measured using a meter bridge. A student chooses the standard resistance S to be 100 $\mathrm{\Omega}$. He finds the null point at l_{1 }= 2.9 cm. He is told to attempt to improve accuracy. Which of the following is a useful way?

1. | He should measure l_{1} more accurately |

2. | He should change S to 1000 Ω and repeat the experiment |

3. | He should change S to 3 Ω and repeat the experiment |

4. | He should give up hope of more accurate measurement with a meter bridge |

Subtopic: Meter Bridge & Potentiometer |

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Two cells of emf's approximately \(5\) V and \(10\) V are to be accurately compared using a potentiometer of length \(400\) cm.

1. | The battery that runs the potentiometer should have a voltage of \(8\) V |

2. | The battery of the potentiometer can have a voltage of \(15\) V and \(R\) adjusted so that the potential drop across the wire slightly exceeds \(10\) V |

3. | The first portion of \(50\) cm of the wire itself should have a potential drop of \(10\) V |

4. | Potentiometer is usually used for comparing resistances and not voltages |

Subtopic: Meter Bridge & Potentiometer |

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A metal rod of length 10 cm and a rectangular cross-section of \(1~ \text {cm} \times 1/2~ \text {cm}\) is connected to a battery across opposite faces. The resistance will be:

1. | maximum when the battery is connected across\(1~ \text {cm} \times 1/2~ \text {cm}\) faces. |

2. | maximum when the battery is connected across \(10~ \text {cm} \times 1~ \text {cm}\) faces. |

3. | maximum when the battery is connected across \(10~ \text {cm} \times 1/2~ \text {cm}\) faces. |

4. | same irrespective of the three faces. |

Subtopic: Derivation of Ohm's Law |

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Which of the following characteristics of electrons determines the current in a conductor?

1. | Drift velocity alone. |

2. | Thermal velocity alone. |

3. | Both drift velocity and thermal velocity. |

4. | Neither drift nor thermal velocity. |

Subtopic: Current & Current Density |

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Kirchhoff's junction rule is a reflection of:

(a) | conservation of the current density vector. |

(b) | conservation of charge. |

(c) | the fact that the momentum with which a charged particle approaches a junction is unchanged (as a vector) as the charged particle leaves the junction. |

(d) | the fact that there is no accumulation of charges at a junction. |

Which of the above statements are correct?

1. | (b) and (c) |

2. | (a) and (c) |

3. | (b) and (d) |

4. | (c) and (d) |

Subtopic: Kirchoff's Current Law |

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