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
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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
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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): 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): 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
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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
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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.
Assertion (A): Potential difference across the battery can be greater than its emf.
Reason (R): When current is taken from battery \(V = \varepsilon – ir\).
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: When a battery is being charged, the terminal voltage is \(V = \varepsilon + Ir\), which is greater than its emf \(\varepsilon\). Reason (R) is also true, as it correctly describes the terminal voltage when the battery is discharging (current is taken from it). However, (R) is not the correct explanation for (A), as (A) refers to a charging scenario (where \(V > \varepsilon\)), while (R) refers to a discharging scenario (where \(V < \varepsilon\)).
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
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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.