Instructions

For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the second decimal place; e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer.

Question 11

Three identical capacitors $$๐ถ_{1}, ๐ถ_{2}$$ and $$๐ถ_{3}$$ have a capacitance of 1.0 $$\mu$$๐น each and they are uncharged initially. They are connected in a circuit as shown in the figure and $$๐ถ_{1}$$ is then filled completely with a dielectric material of relative permittivity $$\epsilon_{r}$$.The cell electromotive force (emf) $$๐‘‰_{0}$$ = 8 ๐‘‰. First the switch $$๐‘†_{1}$$ is closed while the switch $$๐‘†_{2}$$ is kept open. When the capacitor $$๐ถ_{3}$$ is fully charged, $$๐‘†_{1}$$ is opened and $$๐‘†_{2}$$ is closed simultaneously. When all theย capacitors reach equilibrium, the charge on $$๐ถ_{3}$$ is found to be 5 $$\mu$$๐ถ. The value of $$\epsilon_{r}$$ =____________.


Correct Answer: e


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