Consider two insulating sheets with thermal resistances $R_1$ and $R_2$ as shown. The temperatures $\theta $ is
Consider two insulating sheets with thermal resistances $R_1$ and $R_2$ as shown. The temperatures $\theta $ is
- A
$\frac{{{\theta _1}{\theta _2}{R_1}{R_2}}}{{({R_1} + {R_2})({\theta _1} + {\theta _2})}}$
- B
$\frac{{{\theta _1}{R_1} + {\theta _2}{R_2}}}{{{R_1} + {R_2}}}$
- C
$\frac{{({\theta _1} + {\theta _2})\left( {{R_1}{R_2}} \right)}}{{R_1^2 + R_2^2}}$
- D
$\frac{{{\theta _1}{R_2} + {\theta _2}{R_1}}}{{{R_1} + {R_2}}}$
Similar Questions
$A$ metal rod of length $2$$m$ has cross sectional areas $2A$ and $A$ as shown in figure. The ends are maintained at temperatures $100°C$ and $70°C$ . The temperature at middle point $C$ is...... $^oC$
$A$ metal rod of length $2$$m$ has cross sectional areas $2A$ and $A$ as shown in figure. The ends are maintained at temperatures $100°C$ and $70°C$ . The temperature at middle point $C$ is...... $^oC$
Two bars of thermal conductivities $K$ and $3K$ and lengths $1\,\, cm$ and $2\,\, cm$ respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is $0\,^oC$ and $100\,^oC$ respectively (see figure), then the temperature $\varphi $ of the interface is......... $^oC$
Two bars of thermal conductivities $K$ and $3K$ and lengths $1\,\, cm$ and $2\,\, cm$ respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is $0\,^oC$ and $100\,^oC$ respectively (see figure), then the temperature $\varphi $ of the interface is......... $^oC$
Three rods $A, B$ and $C$ of thermal conductivities $K, 2\,K$ and $4\,K$, cross-sectional areas $A, 2\,A$ and $2\,A$ and lengths $2l, l$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100^o\,C, 50^o\,C$, and $0^o\,C$ respectively, then the temperature $\theta$ of the junction is ......... $^oC$
Three rods $A, B$ and $C$ of thermal conductivities $K, 2\,K$ and $4\,K$, cross-sectional areas $A, 2\,A$ and $2\,A$ and lengths $2l, l$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100^o\,C, 50^o\,C$, and $0^o\,C$ respectively, then the temperature $\theta$ of the junction is ......... $^oC$
$A$ wall has two layers $A$ and $B$ made of different materials. The thickness of both the layers is the same. The thermal conductivity of $A$ and $B$ are $K_A$ and $K_B$ such that $K_A = 3K_B$. The temperature across the wall is $20°C$ . In thermal equilibrium
$A$ wall has two layers $A$ and $B$ made of different materials. The thickness of both the layers is the same. The thermal conductivity of $A$ and $B$ are $K_A$ and $K_B$ such that $K_A = 3K_B$. The temperature across the wall is $20°C$ . In thermal equilibrium
$A$ cylinder of radius $R$ made of a material of thermal conductivity ${K_1}$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity ${K_2}$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
$A$ cylinder of radius $R$ made of a material of thermal conductivity ${K_1}$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity ${K_2}$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
- [IIT 1988]