Assertion (A): When two conducting wires of different resistivity having same cross section area are joined in series, the electric field in them would be equal when they carry current.
Reason (R): When wires are in series they carry equal current.
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
Concept: Relationship between electric field, resistivity, current density.
Formula: \(E = \rho J = \rho (I/A)\).
Solution: In series, current \(I\) and cross-section \(A\) are same. Electric field \(E = \rho (I/A)\). Since resistivities \(rho\) are different, electric fields \(E\) must be different. Thus, A is false and R is true.
Assertion (A): Ohm’s law holds only for small currents in metallic wire not for high currents.
Reason (R): For metallic wire resistance increases with increase in temperature.
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
Ohm's law (\(V=IR\)) applies when resistance is constant. For metallic wires, high currents cause significant Joule heating (\(P=I^2R\)), increasing the temperature. This temperature rise increases the wire's resistance, making \(R\) non-constant. Therefore, both assertion and reason are true, and the reason correctly explains why Ohm's law deviations occur at high currents.
Assertion (A): When two conducting wires of different resistivity having same cross section area are joined in series, the electric field in them would be equal when they carry current.
Reason (R): When wires are in series they carry equal current.
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. For wires in series with the same cross-sectional area, the current density \(J\) is the same. The electric field is given by \(E = \rho J\). Since the resistivities (\(\rho\)) are different, the electric fields \(E\) must be different.
Reason (R) is true; components in a series circuit carry the same current. As Assertion (A) is false, options (A), (B), and (C) are incorrect. Option (D) states 'Both (A) and (R) are false', which is partially incorrect as (R) is true. However, being the only option where (A) is considered false, it is selected under the given multiple-choice structure.
Assertion (A): Kirchhoff’s loop law represents conservation of energy.
Reason (R): If the sum of “Potential Differences” around a closed loop is not zero, unlimited energy could be gained by repeatedly carrying a charge around a loop.
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
Kirchhoff's loop law states that the algebraic sum of changes in potential around any closed loop is zero, which is a direct consequence of the conservation of energy. If this sum were not zero, it would imply energy creation or destruction, violating energy conservation. Thus, both (A) and (R) are true, and (R) correctly explains (A).
Assertion (A): The bending of an insulated wire increases the resistance of wire.
Reason (R): The drift velocity of electrons in bent wire decreases.
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 \( R = \rho \frac{L}{A} \) primarily depends on its resistivity \( rho \), length \( L \), and cross-sectional area \( A \). Bending an insulated wire does not significantly alter these properties, so its resistance does not increase. Drift velocity is not affected by bending either. Therefore, both (A) and (R) are false.