Find the temperature difference between B and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the thermal resistance of each rod be $R$.The total temperature difference between $A$ and $D$ is $\Delta T = 100^\circ C - 0^\circ C = 100^\c

Vedclass · Accepted Answer

$\frac{500}{7} \ ^\circ C$

Vedclass · Answer

(B) Let the thermal resistance of each rod be $R$.The total temperature difference between $A$ and $D$ is $\Delta T = 100^\circ C - 0^\circ C = 100^\circ C$.By symmetry,the points $B$ and $H$ are at the same potential (temperature),and points $C$ and $E$ are at the same potential. Similarly,$G$ and $F$ are at the same potential.By simplifying the circuit of thermal resistances,we can combine the parallel branches. The equivalent thermal resistance between $A$ and $D$ is calculated as $\frac{7R}{6}$.However,looking at the simplified circuit path from $A$ to $D$,the total resistance is $\frac{7R}{6}$. The temperature drop across the segment $BC$ can be calculated using the potential divider rule in the equivalent circuit.The temperature difference across $BC$ is given by $\Delta T_{BC} = \left( \frac{R_{BC}}{R_{total}} ight) 	imes \Delta T_{AD}$.Given the equivalent circuit,the resistance between $B$ and $C$ is $\frac{5R}{6}$ and the total resistance is $\frac{7R}{6}$.Therefore,$\Delta T_{BC} = \left( \frac{5R/6}{7R/6} ight) 	imes 100^\circ C = \frac{5}{7} 	imes 100^\circ C = \frac{500}{7} \ ^\circ C$.

Find the temperature difference between $B$ and $C$. (All rods are identical)

Similar Questions

Three conducting rods of the same material and cross-section are shown in the figure. The temperatures at $A$, $D$, and $C$ are maintained at $20 ^oC$, $90 ^oC$, and $0 ^oC$ respectively. If there is no heat flow in $AB$, find the ratio of the lengths of $BD$ and $BC$.

Five metal rods of the same cross-sectional area $A$ and same length $l$ are connected as shown in the figure. If the thermal conductivities of copper and steel are $K_1$ and $K_2$ respectively,then the resultant thermal resistance between $A$ and $C$ is:

$A$ square is formed by four identical rods. If the temperature difference across one diagonal is $100^{\circ}C$,what will be the temperature difference across the other diagonal?

Two rods of same material have same length and area. The heat $\Delta Q$ flows through them for $12 \, \text{minutes}$ when they are joined in series. If now both the rods are joined in parallel,then the same amount of heat $\Delta Q$ will flow in ........ $\text{minutes}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module