7.
The voltage measured across a metal bar is plotted as a function of applied current, at two
different temperatures (T1 and T2). Which of the following statements is correct?
a. T1 is greater than T2
b. T2 is less than T1
c. T1 is equal to T2
d. T1 could be less than or greater than T2 depending on which metal it is
The correct statement is T1 is greater than T2, because the V–I graph at T1 has a steeper slope, which means higher resistance, and resistance of a metallic conductor increases with temperature.
Concept explanation
In a V–I (voltage–current) graph for a conductor, the slope equals resistance R=V/I, so a steeper line means greater resistance. For metallic conductors, resistance increases with temperature because lattice vibrations increase and scatter electrons more, so higher resistance corresponds to higher temperature. In the given figure, line T1 is steeper than line T2, so resistance at T1 is higher and therefore T1 > T2.
Detailed evaluation of options
Option a: T1 is greater than T2
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Slope of V–I graph at T1 is larger than at T2, so R1>R2.
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For metals, higher resistance means higher temperature, hence T1 is greater than T2, making this option correct.
Option b: T2 is less than T1
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Saying “T2 is less than T1” is mathematically the same inequality as option a but reversed in wording; the question expects a single correct choice, and option a directly matches the physical reasoning tied to the steeper T1 line, so option b is not the designated correct answer.
Option c: T1 is equal to T2
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If T1 were equal to T2, both V–I lines would coincide and have the same slope (same resistance).
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The graph clearly shows different slopes, so T1 ≠ T2, and this option is false.
Option d: T1 could be less than or greater than T2 depending on metal
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For ordinary metals, resistance increases monotonically with temperature in the relevant range, so for a given metal a steeper V–I line always corresponds to a higher temperature.
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Since the graph already fixes which line is steeper (T1), the relative order of T1 and T2 is determined and does not depend on which metal is used, so this option is incorrect.
Short, SEO-focused introduction
Voltage–current graphs are a powerful tool for analyzing how a metal bar behaves electrically at two different temperatures, T1 and T2. By examining the slope of each line on the V–I graph, one can determine the resistance at each temperature and correctly infer that T1 is greater than T2 for the given metal bar.
