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 . The cell electromotive force (emf) V0 = 8 V. 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 ∈r = ________

Engineering

Physics

Circuit Analysis Having Capacitor Only

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 $\in_{r}$ . The cell electromotive force (emf) V₀ = 8 V. 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 ∈_r = _________.

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When S₁ (closed) and S₂ (open)

Charge on C₃ = 8 µC

and C₁ and C₂ with be uncharged.

New charge on C₃ = 5 µC so charge on C₁ and C₂ = 3 µC

Applying loop rule for the above circuit

$\frac{5}{1} = \frac{3}{\in_{r}} + \frac{3}{1} \Rightarrow \in_{r} = 1.50$