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While Studying the Dependence of Potential Difference ( V) Across a Resistor on the Current (I) Passing Through It, in Order to Determine the Resistance of the Resistor, - Science

Question

Answer in Brief

Answer the following question.
While studying the dependence of potential difference ( V) across a resistor on the current (I) passing through it, in order to determine the resistance of the resistor, a student took 5 readings for different values of current and plotted a graph between V and t. He got a straight line graph passing through the origin. What does the straight-line signify? Write the method of determining the resistance of the resister using this graph. 

Solution

The straight-line graph between the potential difference ( V) and current(I) shows that resistor is a linear element and follows Ohm's Law.
Calculation of Resistance: At any point on the graph, resistance is given as, 

`"R" = ("V"_° ("value of potential difference at that point"))/("I"_°  ("value of current at that point"))`

In other words, the Slope of the graph at any point gives the value  `1/"R"`
Hence,
slope `="I"_°/"V"_° = 1/"R"`

`⇒ "R" = 1/"slope" =( "V"_° ("Value of Potential difference at that point"))/("I"_°  ("Value of current at that point"))` 

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