Three rods of material x and two rods of material y are connected as shown in figure- All the rods are of identical length and cross - sectional area- The end A is maintained at 100- C and the junction D at 0- C- It is given that resistance of rod of material x is R- Further- K x -2 K y-Match the entries of column I and column IIWline Column- I-Column IIINhlineA- Temperature of junction B-P- Does not behave like all - balanced - wheatstone-s bridgelllhlineB- Temperature of junction C-Q- Is twice of the other-lllhlineC- This network is-R- - frac 4007 degree celsiusllhhlinelendarray A- A-P - B-R C-P D-R - B- A-P B-Q C-P D-R - C- A-R B-S C-P D-Q - D- A-Q B-Q C-Q D-P -

The correct option is C A R B S C P D Q Thermal resistance R = l/KA If K_x=2K_y,R_x=R_y/2 (or) R_y=2R_x=2R So, final diagram will be, ...

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Byju's Answer

Standard XII

Physics

Reverse Bias

Three rods of...

Question

Three rods of material x and two rods of material y are connected as shown in figure. All the rods are of identical length and cross – sectional area. The end A is maintained at $100^{\circ} C$ and the junction D at $0^{\circ} C$ . It is given that resistance of rod of material x is R. Further, $K_{x} = 2 K_{y}$ .

Match the entries of column I and column II
$\begin{matrix} C o l u m n - I & C o l u m n I I A . T e m p e r a t u r e o f j u n c t i o n B & P . D o e s n o t b e h a v e l i k e a b a l a n c e d w h e a t s t o n e^{'} s b r i d g e B . T e m p e r a t u r e o f j u n c t i o n C & Q . I s t w i c e o f t h e o t h e r . C . T h i s n e t w o r k i s & R . \frac{400}{7} d e g r e e c e l s i u s D . R e s i s t a n c e o f r o d o f m a t e r i a l y & S . \frac{300}{7} d e g r e e c e l s i u s \end{matrix}$

A-P B-R C-P D-R

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A-P B-Q C-P D-R

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A-R B-S C-P D-Q

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A-Q B-Q C-Q D-P

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Solution

The correct option is C A-R B-S C-P D-Q

Thermal resistance $R = \frac{l}{K A}$
If $K_{x} = 2 K_{y}, R_{x} = \frac{R_{y}}{2} (o r) R_{y} = 2 R_{x} = 2 R$
So, final diagram will be,
By the logic of current, for point B,
$\frac{T_{1} - 100}{R} + \frac{T_{1} - T_{2}}{R} + \frac{T_{1} - 0}{2 R} = 0$
$\Rightarrow 2 T_{1} - 200 + 2 T_{1} - 2 T_{2} + T_{1} = 0$
$\Rightarrow 5 T_{1} - 2 T_{2} = 200 \to (1)$
For point C, $\frac{(T_{2} - 100)}{2 R} + \frac{(T_{2} - T_{1})}{R} + \frac{(T_{2} - 0)}{R} = 0 \Rightarrow 5 T_{2} - 2 T_{1} = 100 \to (2)$
Solving (1) and (2), we get,
$T_{1} = \frac{400^{\circ} C}{7}$ and $T_{2} = \frac{300^{\circ} C)}{7}$
Thermal resistance between B and D is,

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Similar questions

Three rods of material x and two rods of material y are connected as shown in figure. All the rods are of identical length and cross - sectional area. The end A is maintained at 100 $^{\circ}$ C and the junction C at 0 $^{\circ}$ C. It is given that resistance of rod of material x is R. Further, $K_{x}$ = ${2 K}_{y}$ .

Match the entries of column I and column II

$\begin{matrix} c o l u m n 1 & c o l u m n 2 A . T e m p e r a t u r e o f j u n c t i o n B & P . D o e s n o t b e h a v e l i k e a b a l a n c e d w h e a t s t o n e s^{'} s b r i d g e B . T e m p e r a t u r e o f j u n c t i o n C & Q . I s t w i c e o f t h e o t h e r C . T h i s n e t w o r k i s & R . {\frac{400}{7}}^{\circ} C D . R e s i s t a n c e o f r o d o f m a t e r i a l y & S . {\frac{300}{7}}^{\circ} C \end{matrix}$

Match the column I with column II
In the circuit shown in fig. $C_{1} = C, C_{2} = 2 C, C_{3} = 3 C a n d C_{4} = 4 C$

$\begin{matrix} C o l u m n - I & C o l u m n - I I (A) M a x i m u m p o t e n t i a l d i f f e r e n c e & (P) a c r o s s C_{1} (B) M i n i m u m p o t e n t i a l d i f f e r e n c e & (Q) a c r o s s C_{2} (C) M a x i m u m p o t e n t i a l e n e r g y & (R) a c r o s s C_{3} (D) M i n i m u m p o t e n t i a l e n e r g y & (S) a c r o s s C_{4} \end{matrix}$

Q. Three rods of material

X

and three rods of material

Y

are connected as shown in figure. All the rods are identical in length and cross-sectional area. If the end

A

is maintained at

60^{\circ} C

and the junction

E

10^{\circ} C

, calculate the temperatures of the junctions

B, C, D

. The thermal conductivity of

X

0.92

C G S

units and that of

Y

0.46 C G S

units.

Q. Three rods of material

X

and three of material

Y

are connected as shown in figure. All the rods are identical in length and cross-sectional area. If the end

A

is maintained at

60^{\circ} C

and the junction

E

10^{\circ} C

, calculate the temperature at the junction

B

. The thermal conductivity of

X

800 {Wm}^{- 1}

^{\circ} C^{- 1}

and that of

Y

400 {Wm}^{- 1}

^{\circ} C^{- 1}

Three rods of material x and three of material y are connected as shown in figure. All the rods are identical in length and cross-sectional area. If the end A is maintained at 60 $^{\circ}$ C and the junction E at 10 $^{\circ}$ C, calculate the temperature of the junction B. The thermal conductivity of x is 800 W/M- $^{\circ}$ C and

that of y is 400 W/M- $^{\circ}$ C

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