First slide

Capacitance

Question

For the circuit shown, which of the following statements is true ?

Moderate

A

With S₁ closed, V₁ = 15 V,V₂ = 20 V
B

With S₃ closed, V₁ = V₂ = 25V
C

With S₁ and S₂ closed, V₁ = V₂ = 0
D

With S₁ and S₃ closed, V₁ = 30 V, V₂ = 20 V

Solution

Let us consider the first alternative. When switch S₁ is closed, the charge on plate 2 will not change because this plate remains isolated. Hence the bound charge on plate
will not change. Thus, the potential difference across C₁ will remain the same.
Similarly, when S₃ is closed, V₁ and V₂ do not change. When S₁ and S₂ are closed, the charge on plates 2 and 3 will not change. So, the bound charges on plates 1 and 4 will not change. Thus, V₁ and V₂ remain the same. With S₁ and S₃ closed, the charge on plate 4 will remain the same. So, the bound charges on plates will not change. Thus, V₁ and V₂ remain the same.

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