Space between two concentric spheres of radii r1 and r2- such that r1 - r2- is filled with a material of resistivity - Find the resistance between inner and outer surface of the material-

The correct option is B r_2 r_1r_1r_2ρ4π Given, #160;Radii of the concentric sphere s, r_1 and r_2 #160; #160; #160; #160; #16 ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Conductivity and Resistivity

Space between...

Question

Space between two concentric spheres of radii $r_{1}$ and $r_{2}$ , such that $r_{1} < r_{2}$ , is filled with a material of resistivity $ρ$ . Find the resistance between inner and outer surface of the material.

\frac{r_{1}}{r_{2}} \frac{ρ}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{r_{2} - r_{1}}{r_{1} r_{2}} \frac{ρ}{4 π}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{r_{1} r_{2}}{r_{2} - r_{1}} \frac{ρ}{4 π}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{r_{2} - r_{1}}{r_{1} r_{2}} \frac{ρ}{4 π}$
Given,
Radii of the concentric sphere s, $r_{1}$ and $r_{2}$ [ $r_{1} < r_{2}$ ]
Resistivity of the material $= ρ$
As we know,
Resistance can be given by the formula,
$R = ρ \frac{l}{A}$
In this case,
length of the resistor here it's radius, $l = r$
and Area of the spherical resistor, $A = 4 π r^{2}$
$∴ R = ρ \frac{d r}{4 π r^{2}}$
[where $r$ is any radius and $d r$ is small element]
Total resistance,
$R = \frac{ρ}{4 π} \int_{r_{1}}^{r_{2}} \frac{d r}{r^{2}}$
$\Rightarrow R = \frac{ρ}{4 π} {[- \frac{1}{r}]}_{r_{1}}^{r_{2}}$
$\Rightarrow R = \frac{ρ}{4 π} [\frac{1}{r_{1}} - \frac{1}{r_{2}}]$

$\Rightarrow R = [\frac{r_{2} - r_{1}}{r_{1} r_{2}}] \frac{ρ}{4 π}$
Hence, the correct option is $(B)$

Suggest Corrections

Similar questions

Q. Two resistances

R_{1}

and

R_{2}

are made of different materials. The temperature coefficient of the material of

R_{1}

α

and that of material of

R_{2}

- β

. The material of

R_{1}

and

R_{2}

will not change with temperature if

\frac{R_{1}}{R_{2}}

equal to

Q. The resistances

R_{1}

and

R_{2}

are connected in parallel. The equivalent resistance

R_{p}

of the combination is:

(a)

R_{1} + R_{2}

(b)

R_{1} - R_{2}

(c)

\frac{R_{1} R_{2}}{R_{1} + R_{2}}

(D)

\frac{R_{1} + R_{2}}{R_{1} R_{2}}

Q. Two resistances

R_{1}

and

R_{2}

are made of different materials. The temperature coefficient of the material of

R_{1}

α

and that of the material of

R_{2}

- β

. The resistance of the series combination of

R_{1}

and

R_{2}

does not change with temperature, then the ratio of resistances of the two wires

\frac{R_{1}}{R_{2}}

0^{\circ} C

will be :

Q. Three circles of radii

r_{1}

r_{2}

and

r_{3}

are drawn concentric to each other. The radii

r_{1}

and

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}

and

r_{1}

. The area between the circles of radii

r_{3}

and

r_{2}

is equal to the area between the circles of radii

r_{2}

and

r_{1}

What is the value of

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

Q. Find the centre of mass of a uniform plate having semicircular inner and outer boundaries of radii

R_{1}

and

R_{2}

(figure 9 - E5)

Join BYJU'S Learning Program

Space between two concentric spheres of radii r1 and r2, such that r1<r2, is filled with a material of resistivity ρ. Find the resistance between inner and outer surface of the material.

Space between two concentric spheres of radii $r_{1}$ and $r_{2}$ , such that $r_{1} < r_{2}$ , is filled with a material of resistivity $ρ$ . Find the resistance between inner and outer surface of the material.