1. Use steady-state heat flow concept

   Two insulating sheets are in series for heat conduction, with thermal resistances $R_1$ and $R_2$.

   Let the junction temperature be $\theta$.

   Top temperature $= \theta_1$, bottom temperature $= \theta_2$.

   In steady state, the heat current through both sheets is the same.

2. Write heat current through each sheet

   Through the first sheet: $q = \frac{\theta_1-\theta}{R_1}$

   Through the second sheet: $q = \frac{\theta-\theta_2}{R_2}$

3. Equate the two heat currents

   $\frac{\theta_1-\theta}{R_1} = \frac{\theta-\theta_2}{R_2}$

4. Cross multiply

   $R_2(\theta_1-\theta) = R_1(\theta-\theta_2)$

   $R_2\theta_1 - R_2\theta = R_1\theta - R_1\theta_2$

5. Collect terms containing $\theta$

   $R_2\theta_1 + R_1\theta_2 = R_1\theta + R_2\theta$

   $R_2\theta_1 + R_1\theta_2 = (R_1+R_2)\theta$

6. Solve for junction temperature

   $\theta = \frac{\theta_1R_2 + \theta_2R_1}{R_1+R_2}$

7. Match with options

   This matches: $\boxed{\frac{\theta_1R_2 + \theta_2R_1}{R_1+R_2}}$

   So, Option A is correct.

8. Check other options briefly

   • B incorrectly puts same resistance with same-side temperature.
   • C and D have incorrect denominator form $(R_2-R_1)$, which does not arise in series thermal resistance.

Therefore, the correct answer is A.