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

1. | number of charge carriers can change with temperature T |

2. | the time interval between two successive collisions can depend on T |

3. | length of material can be a function of T |

4. | 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 ${\mathrm{R}}_{2}$ = 10 $\mathrm{\Omega}$ and ${\mathrm{R}}_{1}$ =5 $\mathrm{\Omega}$. The other student takes ${\mathrm{R}}_{2}$ =1000 $\mathrm{\Omega}$ and ${\mathrm{R}}_{1}$ =500 $\mathrm{\Omega}$. In the standard arm, both take ${\mathrm{R}}_{3}$ = 5 $\mathrm{\Omega .}$

Both find $\mathrm{R}=\frac{{\mathrm{R}}_{2}}{{\mathrm{R}}_{1}}{\mathrm{R}}_{3}=10\mathrm{\Omega}$ 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 ${\mathrm{R}}_{2}$ and ${\mathrm{R}}_{1}$ can be measured.

(c) If the student uses large values of ${\mathrm{R}}_{2}$ and ${\mathrm{R}}_{1}$, 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.

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 I) in the shape of a circle. Note that as the current progresses along the wire, the direction of j (current density) changes in an exact manner, while the current 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 cm x 1/2 cm is connected to a battery across opposite faces. The resistance will be:

1. | maximum when the battery is connected across 1 cm x 1/2 cm faces. |

2. | maximum when the battery is connected across 10 cm x 1 cm faces. |

3. | maximum when the battery is connected across 10 cm x 1/2 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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