Question

In the figure shown, the voltage across C₃ will be 

Options

• `("C"_2"V")/("C"_1 + "C"_2 + "C"_3)`

• `("C"_1"V")/("C"_1 + "C"_2 + "C"_3)`

• `("C"_3"V")/("C"_1 + "C"_2 + "C"_3)`

• `(("C"_1 + "C"_2)"V")/("C"_1 + "C"_2 + "C"_3)`

Answer 1

`(("C"_1 + "C"_2)"V")/("C"_1 + "C"_2 + "C"_3)`

Explanation:

Q = (C₁ + C₂)V₁ = C₃V₂    V₁ + V₂ = V

`therefore ("C"_1 + "C"_2)/"C"_3 = "V"_2/"V"_1    "C"_3/("C"_1 + "C"_2) = "V"_1/"V"_2`

`("C"_1 + "C"_2 + "C"_3)/("C"_1 + "C"_2) = ("V"_1 + "V"_2)/"V"_2 = "V"/"V"_2`

`therefore "V"_2 = ("V"("C"_1 + "C"_2))/("C"_1 + "C"_2 + "C"_3)`