Assertion (A): The average thermal velocity of the electrons in the conductor is zero.
Reason (R): Direction of motion of electrons are randomly oriented.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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In a conductor, free electrons are in constant random thermal motion. Due to this random orientation, for every electron moving in one direction, there's another moving in a roughly opposite direction, leading to a cancellation of their velocities. Therefore, the vector sum of these random velocities, which is the average thermal velocity, is zero. Both (A) and (R) are true, and (R) correctly explains (A).
Assertion (A): In series combination of electrical bulb, lower power bulb emits more light than that of higher power bulb.
Reason (R): The lower power bulb in series gets more current than the higher power bulb.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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In a series circuit, the current \( I \) is the same for all components. The power dissipated by a bulb is given by \( P = I^2 R \). A lower power bulb has a higher resistance \( (R = V^2/P) \). Thus, it dissipates more power and glows brighter in series. Reason (R) is false because the current is the same for all bulbs in series.
Assertion (A): A galvanometer can be used as an ammeter only.
Reason (R): A galvanometer can be used in electric circuit to detect the electric current only.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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A galvanometer is a device used to detect small electric currents. It can be converted into an ammeter by connecting a low resistance shunt in parallel or into a voltmeter by connecting a high resistance in series. Therefore, the assertion that it can be used 'only' as an ammeter is false, and the reason that it can be used to detect current 'only' is also false. Thus, both A and R are false.
Assertion (A): The average thermal velocity of the electrons in a conductor is zero.
Reason (R): In the absence of an electric field, the electrons are at rest.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Assertion (A) is true: The thermal motion of electrons is random, so their average velocity vector \( langle vec{v}_{th} rangle \) is zero. Reason (R) is false: Electrons in a conductor are in continuous, random thermal motion even in the absence of an external electric field; they are not at rest.
Assertion (A): The resistivity of a semiconductor increases with temperature.
Reason (R): The atoms of a semiconductor vibrate with larger amplitude at higher temperature thereby increasing its resistivity.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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For a semiconductor, resistivity actually \(\text{decreases}\) with increasing temperature because more charge carriers (electrons and holes) are generated. The reason given describes the behavior of conductors, where increased atomic vibrations impede electron flow, increasing resistivity. Thus, both Assertion (A) and Reason (R) are false for a semiconductor.
Assertion (A): The connecting wires are made of copper.
Reason (R): Copper is a superconductor at room temperature.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Assertion (A) is true: Copper is widely used for connecting wires due to its excellent electrical conductivity and ductility. Reason (R) is false: Copper is a good conductor but not a superconductor at room temperature; it exhibits electrical resistance. Superconductivity typically occurs at very low temperatures for specific materials.
Assertion (A): As a wire is stretched to four times its length, its resistivity becomes four times, such that resistance also increases.
Reason (R): \( R = \frac{\rho A}{l} \) where symbols have their usual meaning.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is false because resistivity is an intrinsic property of the material and does not change with stretching, only resistance changes. Reason (R) is false because the correct formula for resistance is \( R = \frac{\rho l}{A} \).
Assertion (A): Arrows indicating current in different branches of a circuit follow vector- addition laws.
Reason (R): Current is a scalar quantity but it adds like vector.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is false because current is a scalar quantity and its addition follows Kirchhoff's current law (algebraic sum), not vector addition. Reason (R) is false because while current is a scalar, it does not add like a vector; it adds algebraically.
Assertion (A): As temperature of an electrolyte is increased, its conductivity increases.
Reason (R): Increase of temperature makes the electrolyte less viscous.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true. For electrolytes, increased temperature leads to more ion dissociation and reduced viscosity. Reason (R) is true as increased temperature reduces viscosity. (R) correctly explains (A) as lower viscosity allows ions to move more freely, increasing conductivity.
Assertion (A): Electric appliances with a metallic body have three pin connections whereas an electric bulb has two pin connections.
Reason (R): Three pin connection reduces heating of connecting cable.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true. Metallic-bodied appliances require a third pin for earthing for safety. Electric bulbs usually do not. Reason (R) is false. The third pin (earth) is for safety, to prevent electric shock in case of a fault, not to reduce cable heating.