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): 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): 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): 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): As temperature of an electrolyte is increased, its conductivity increases.
Reason (R): Increase of temperature makes the electrolyte less viscous.
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 electrolytes, increased temperature leads to more ion dissociation and reduced viscosity. Reason (R) is true as increased temperature reduces viscosity. (R) correctly explains (A) as lower viscosity allows ions to move more freely, increasing conductivity.
Assertion (A): The resistivity of a semiconductor decreases with increase in temperature.
Reason (R): In a conductor, the rate of collisions between free electrons and ions increases with increase of 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 true. Increased temperature in semiconductors generates more charge carriers, decreasing resistivity. Reason (R) is also true, as thermal vibrations increase electron-ion collisions in conductors, increasing resistivity. However, (R) explains conductors, not semiconductors, so it's not the correct explanation for (A).