Assertion (A): When a wire is stretched, then its resistance changes directly as square of its length.
Reason (R): When wire is stretched its thickness/ radius decreases and volume remains constant.
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
View Answer
Resistance of a wire is given by \(R = rho L/A\), where \(rho\) is resistivity, \(L\) is length, and \(A\) is cross-sectional area. When a wire is stretched, its volume \(V = AL\) remains constant. So, \(A = V/L\). Substituting this into the resistance formula, we get \(R = rho L / (V/L) = rho L^2 / V\). Since \(rho\) and \(V\) are constant, \(R propto L^2\). Thus, Assertion (A) is true. When stretched, the length increases, and for constant volume, the cross-sectional area (and thus thickness/radius) must decrease. So, Reason (R) is true. Reason (R) correctly explains why \(R propto L^2\).
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
View Answer
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): 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
View Answer
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
View Answer
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
View Answer
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): 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
View Answer
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): If an observer is moving with drift speed of electrons in direction opposite to current, observer will not experience any magnetic field.
Reason (R): In the frame of observer charged particles in conductor 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
View Answer
If an observer moves with the electron drift speed (in the direction of electron flow), electrons are at rest relative to them. However, the positive lattice ions, which were stationary in the conductor's frame, are now moving. This motion of positive ions constitutes a current and produces a magnetic field.
Thus, (A) is false. Also, in this frame, only electrons are at rest, while positive ions are moving, so (R) is false.