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Conductivity and Resistivity

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Question

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. What is the relation between $R_{1}, R_{2}$ and $R_{3}$ ?

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Solution

Resistance of each wire is given by $R = \frac{V}{I}$
= Slope of the V-I graph
From the given graph, it is clear that the slope is highest for $R_{1}$ and least for $R_{3}$ .
Hence, we can conclude that $R_{1} > R_{2} > R_{3}$

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Q. Question 11
A student carries out an experiment and plots the V-I graph of three samples of nichrome wire with resistances R1, R2 and R3 respectively (Figure). Which of the following is true?

(a) R1 = R2 = R3
(b) R1 > R2 > R3
(c) R3 > R2 > R1
(d) R2 > R3 > R1

Q. Assertion :In a

△ A B C

a < b < c

r

is inradius and

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

are the axradii opposite to angle

A, B, C

respectively, then

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}

Q. Three circles

C_{1}, C_{2}

C_{3}

r_{1}, r_{2}

r_{1} + r_{2}

respectively are such that

C_{1}

C_{2}

touch each other externally and

C_{3}

internally. Another circle with radius

r_{3}

touches all the three circles. If

r_{1} > r_{2} > r_{3}

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

are in A.P. then

{(\frac{r_{1}}{r_{2}})}^{3}

L - C - R

, graph between peak current and frequency (

ω

) shown in the figure below.
The correct order for

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

Q. Three circles of radii

r_{1}

r_{2}

r_{3}

are drawn concentric to each other. The radii

r_{1}

r_{2}

are such that the area of the circle with radius

r_{1}

is equal to the area between the circles of radii

r_{2}

r_{1}

. The area between the circles of radii

r_{3}

r_{2}

is equal to the area between the circles of radii

r_{2}

r_{1}

What is the value of

r_{1} : r_{2} : r_{3}

?

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