Three identical capacitors $$C1$$,$$C2$$ and $$C3$$ have a capacitance of $$1.0$$μF each and they are uncharged initially. They are connected in a circuit as shown in the figure and $$C1$$ is then filled completely with a dielectric material of relative permittivity εr . The cell electromotive force (emf) $$V0=8V$$ . First the switch $$S1$$ is closed while the switch $$S2$$ is kept open. When the capacitor $$C3$$ is fully charged, $$S1$$ is opened and $$S2$$ is closed simultaneously. When all the capacitors reach equilibrium, the charge on $$C3$$ is found to be $$5$$μC .The value of ε$$r=$$

Question

Three identical capacitors  $$C1$$,$$C2$$ and $$C3$$ have a capacitance of $$1.0$$μF each and they are uncharged initially.  They are connected in a circuit as shown in the figure and  $$C1$$ is then filled completely with a dielectric material of relative permittivity εr  . The cell electromotive force (emf) $$V0=8V$$ . First the switch $$S1$$ is closed while the switch $$S2$$ is kept open. When the capacitor $$C3$$ is fully charged, $$S1$$ is opened and  $$S2$$  is closed simultaneously. When all the capacitors  reach  equilibrium,  the  charge  on $$C3$$  is  found  to  be  $$5$$μC .The  value of ε$$r=$$

Infinity Learn · Accepted Answer

Applying loop rule $$51$$−$$3$$εr−$$31=0$$       ⇒$$3$$ε$$r=2$$⇒ε$$r=1.50$$

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