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Resistance

A student car...

Question

Question 11
A student carries out an experiment and plots the V-I graph of three samples of nichrome wire with resistances $R_{1}$ , $R_{2}$ and $R_{3}$ respectively (figure). Which of the following is true?

(a) $R_{1} = R_{2} = R_{3}$
(b) $R_{1} > R_{2} > R_{3}$
(c) $R_{3} > R_{2} > R_{1}$
(d) $R_{2} > R_{3} > R_{1}$

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Solution

(c) $R_{3} > R_{2} > R_{1}$

From the graph it is clear that for a fixed value of voltage the value of current for $R_{1}$ is greater than $R_{2}$ and $R_{3}$ . We know that for a fixed value of voltage, current is inversely proportional to resistance. Hence $R_{3}$ has the highest resistance and $R_{1}$ has the least resistance.

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R_{1}, R_{2}

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△ A B C

a < b < c

r

r_{1}, r_{2}, r_{3}

A, B, C

r < r_{1} < r_{2} < r_{3}

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

\frac{R_{1}}{r_{1}} + \frac{R_{2}}{r_{2}} + \frac{R_{3}}{r_{3}} =

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r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = Δ^{2}

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ω

R_{1}, R_{2} a n d R_{3}

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