Assertion (A): The current density \( \vec{J} \) at any point in ohmic resistor is in direction of electric field \( \vec{E} \) at that point.
Reason (R): A point charge when released from rest in a region having only electrostatic field always moves along electric lines of force.
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 from \( \vec{J} = \sigma \vec{E} \) where \( \sigma \) is conductivity. Reason (R) is false because a charge released from rest moves along an electric field line only if the field line is straight, which is not always true.
Assertion (A): The drift speed of electrons in metals is small (in the order of a few \(mm/s\)) and the charge of an electron is also very small (\(= 1.6 \times 10^{-19}\text{ C}\)), yet we can obtain a large current in a metal.
Reason (R): At room temperature, the thermal speed of electron is very high (about \(10^7\) times the drift speed).
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
Despite small drift speed \(v_d\) and electron charge \(e\), metals have a very high number density \(n\) of free electrons. This high \(n\) allows for large current \(I\). Thermal speed is irrelevant to the magnitude of current. So, A is true, R is true, but R does not explain A.
Assertion (A): The drift speed of electrons in metals is small (in the order of a few \(mm/s\)) and the charge of an electron is also very small (\(= 1.6 \times 10^{-19} C\)), yet we can obtain a large current in a metal.
Reason (R): At room temperature, the thermal speed of electron is very high (about \(10^7\) times the drift speed).
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 is true because metals have a very high density of free electrons (\(n\)). The current is given by \(I = n A v_d e\), and a large \(n\) allows for a large current even with small \(v_d\) and \(e\). Reason is also true as thermal speeds are much higher than drift speeds. However, the high thermal speed does not explain why large currents are obtained.
Assertion (A): As drift velocity increases current flowing through conductor decreases.
Reason (R): Current flowing through conductor is inversely proportional to drift velocity.
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
The relation between current (I) and drift velocity \(v_d\) is \(I = nAe v_d\), where (n) is carrier density, (A) is cross-sectional area, and (e) is electron charge. This equation shows that current is directly proportional to drift velocity. Therefore, both Assertion (A) and Reason (R) are false.
Assertion (A): Current flows in conductor only when there an electric field is applied to a conductor.
Reason (R): Drift velocity of \(e^-\) decreases in presence of electric field.
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 true: A net flow of charge (current) in a conductor requires an external electric field to give the free electrons a directional drift. Without a field, electron motion is random, leading to zero net current.
Reason (R) is false: In the presence of an electric field, free electrons experience a force and acquire a net drift velocity in the direction opposite to the electric field. Thus, drift velocity increases, it does not decrease.
Assertion (A): The electric bulb glows immediately when switch is on.
Reason (R): The drift velocity of electrons in a metallic wire is very high (near speed of light).
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 because the electric field propagates very quickly, causing electrons to move almost instantly. Reason (R) is false; the drift velocity of electrons is very slow, typically \( 10^{-4} \text{ m/s} \) to \( 10^{-5} \text{ m/s} \).
Assertion (A): Electrolyte are more conducting than metal.
Reason (R): Ions moves faster than electrons.
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 false; metals are generally far better conductors than electrolytes. Reason (R) is also false; electrons typically move faster than ions, and metals have a much higher density of charge carriers.
Assertion (A): Electric field is present in the vicinity of a current carrying wire.
Reason (R): The principle of conservation of charge is not followed, when charges are in motion.
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; an electric field is necessary to drive current through a wire. Reason (R) is false; the principle of conservation of charge is a fundamental law and holds true even when charges are in motion.
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
View Answer
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 \( R = \frac{\rho l}{A} \).