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
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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
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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): In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
Reason (R): Resistance of a metal decreases 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: Meter Bridge principle, temperature dependence of resistance.
Formula: \(R_X / R_S = l_1 / (100 - l_1)\). For metals, \(R\) increases with \(T\).
Solution: When unknown resistance \(R_X\) (metal) is heated, its resistance increases. To maintain the same null point \(l_1\), the standard resistance \(R_S\) must also increase. Assertion (A) is false as it suggests decreasing \(R_S\). Reason (R) is also false as metal resistance increases, not decreases, with temperature.
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): 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. 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
For most resistors, resistance \(R\) increases with temperature. When connected to a battery, the voltage \(V\) is constant. According to Ohm's law, \(I = V/R\). As \(R\) increases due to temperature, the current \(I\) must decrease. Thus, both assertion and reason are true, and the reason correctly explains the assertion.
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): In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
Reason (R): Resistance of a metal decreases 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
Assertion (A) is false. If the unknown resistance (presumably metallic) is heated, its resistance increases. To maintain the null point at the same position in a Meter Bridge (\(R_{\text{unknown}} / R_{\text{standard}} = L_1 / L_2\)), the standard resistance must also be *increased* proportionally, not decreased. Reason (R) is false. For metals, resistance generally *increases* with an increase in temperature, not decreases.
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. 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. For two identical cells (emf \(E\), internal resistance \(r\)), in series, \(E_{\text{eq}} = 2E\) and \(r_{\text{eq}} = 2r\). Max power \(P_{\text{max,s}} = (2E)^2 / (4 \cdot 2r) = E^2 / (2r)\). In parallel, \(E_{\text{eq}} = E\) and \(r_{\text{eq}} = r/2\). Max power \(P_{\text{max,p}} = E^2 / (4 \cdot r/2) = E^2 / (2r)\). The maximum power is indeed the same. Reason (R) is false. For series, the load resistance for max power is \(R_L = 2r\), while for parallel, it is \(R_L = r/2\). These are not the same.