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
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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): 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
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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
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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
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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
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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.
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
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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): power consumed in circuit is maximum when current in circuit is maximum.
Reason (R): Current in circuit is maximum when power consumed by load is maximum.
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
Power consumed by the external resistor (R) is \(P = I^2R = \left(\frac{E}{R+r}\right)^2 R\). Maximum power is delivered to the load when the external resistance equals the internal resistance R=r, according to the maximum power transfer theorem. Maximum current occurs when (R=0). Therefore, both Assertion (A) and Reason (R) are false.
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
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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): Drift velocity of \(e^-\) in a metallic wire will decrease if temperature of wire is increased.
Reason (R): On increasing temperature conductivity of metallic wire decreases.
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
When temperature increases, thermal vibrations of atoms in the conductor increase, leading to more frequent collisions for electrons. This reduces the relaxation time \(\tau\), which in turn decreases the drift velocity \(v_d = \frac{eE\tau}{m}\). Decreased drift velocity leads to decreased conductivity \(\sigma = \frac{ne^2\tau}{m}\). Thus, both (A) and (R) are true, and (R) is the correct explanation for (A).
Assertion (A): In \(R = R_0(1 + \alpha\Delta T)\) when temp. is increased from \(27^\circ C\) to \(227^\circ C\) resistance increases from \(100 \Omega\) to \(150 \Omega\) this implies \(\alpha = 2.5 \times 10^{-3} /^{\circ} C\).
Reason (R):
(R = R_0(1 + \alpha\Delta T)\) is valid only when change in temp \(\Delta T\) is very small i.e. \(\Delta R = (R-R_0) \ll R_0\).
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 (A): \(\Delta T = 227 - 27 = 200^\circ C\). Given \(R=150 \Omega\) and \(R_0=100 \Omega\). Using \(R = R_0(1 + \alpha\Delta T)\) \(\Rightarrow 150 = 100(1 + \alpha \times 200)\) \(\Rightarrow 1.5 = 1 + 200\alpha\) \(\Rightarrow 0.5 = 200\alpha\) \(\Rightarrow \alpha = 2.5 \times 10^{-3} /^{\circ} C\). So, (A) is true. For (R): The formula \(R = R_0(1 + \alpha\Delta T)\) is an empirical approximation for temperature dependence of resistance. It is often used for significant temperature changes and is not strictly limited to very small \(\Delta T\) or \(\Delta R \ll R_0\). Thus, (R) is false.