Assertion (A): When constant current is passing through a conductor of variable area of cross section, electric field inside conductor is inversely proportional to cross sectional area.
Reason (R): Microscopic form of Ohm’s law is \( \vec{E} = \rho \vec{J} \), where \( \vec{E} \) stands for electric field, \( \rho \) stands for resistivity and \( \vec{J} \) stands for current density.
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 because \( I = JA \) and \( E = \rho J \) imply \( E = \frac{\rho I}{A} \). Reason (R) is true as it's the microscopic form of Ohm's law. Reason correctly explains assertion.
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
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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 rate at which energy is being delivered to a light bulb is lower after it has been on for a few seconds than just after it is turned on.
Reason (R): As the filaments warms up, its resistance rises and the current falls.
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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Concept: Resistance of metals increases with temperature. Power \(P = V^2/R\).
Formula: \(P = V^2/R\), \(R \propto T\).
Solution: As filament warms, its resistance \(R\) increases. For constant voltage \(V\), current \(I = V/R\) decreases, so power \(P = V^2/R\) delivered to the bulb also decreases. Thus, A and R are true and R explains A.
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. (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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Concept: Ohm's law states \(V = IR\) with constant \(R\). Resistance of metals depends on temperature.
Formula: \(R_T = R_0(1 + \alpha T)\).
Solution: For high currents, metallic wires heat up significantly, increasing their resistance. This violates the constant resistance assumption of Ohm's law. Therefore, Ohm's law holds for small currents where heating is negligible. A and R are true, and R explains 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 (\(= 1.6 \times 10^{-19}\text{ C}\)), 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): If a resistor is connected to a battery, the current decreases when the temperature increases.
Reason (R): For most of the resistors, resistance increases with increase in 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
Concept: Ohm's law, temperature dependence of resistance.
Formula: \(I = V/R\), \(R\) increases with \(T\) for most resistors.
Solution: For most metallic resistors, resistance \(R\) increases with increasing temperature \(T\). When connected to a battery (constant voltage \(V\)), the current \(I = V/R\) decreases as \(R\) increases. Thus, A and R are true and R explains A.
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
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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): Two identical cells are connected in (a) series (b) parallel then maximum power transferred to the load is same in both cases.
Reason (R): Value of load resistance for maximum power transfer for series and parallel combination of cells are same.
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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Concept: Maximum power transfer theorem for cells.
Formula: For a source with EMF \(E_{eq}\) and internal resistance \(r_{eq}\), maximum power is transferred when load \(R_L = r_{eq}\), and \(P_{max} = \frac{E_{eq}^2}{4r_{eq}}\).
Solution: For 2 cells in series: \(E_{eq} = 2E\), \(r_{eq} = 2r\). \(P_{max, series} = \frac{(2E)^2}{4(2r)} = \frac{E^2}{2r}\). Load \(R_L = 2r\).
For 2 cells in parallel: \(E_{eq} = E\), \(r_{eq} = r/2\). \(P_{max, parallel} = \frac{E^2}{4(r/2)} = \frac{E^2}{2r}\). Thus, maximum power transferred is same, so A is true. Load resistances for max power transfer are different, so R is false.
Assertion (A): The rate at which energy is being delivered to a light bulb is lower after it has been on for a few seconds than just after it is turned on.
Reason (R): As the filaments warms up, its resistance rises and the current falls.
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
Initially, the bulb's cold filament has lower resistance. As it heats up, resistance increases, causing current to drop (for a constant voltage source). Since power \(P = V^2/R\), an increase in \(R\) leads to a decrease in \(P\). Therefore, both assertion and reason are true, and the reason correctly explains the assertion.
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.