A metal plate of thickness 2 ~mm and area 36 mm ^2 - is slide in to a parallel plate capacitor of plate spacing 6 ~mm and area 36 cm ^2 . The metal plate is at a distance 3 ~mm from one of the plates. What is the capacitance of this arrangement? (Let I 4 E ₀ =9 10^9 Nm ^2 C ⁻² )

Step-by-step solution

When metal plate of thickness 2 ~mm is inserted into a parallel plate capacitor, then the arrangement is shown as, Given, thickness of plate, t=2 ~mm and area, A=36 cm ^2 The above circuit can be redrawn as, where, C₁= ₀ A d₁ and C₂= ₀ A d₂ Now, C_ eq = C₁ C₂ C₁+C₂ (In the series combination) aligned & C_ eq = ₀ A [ 1 d₁ 1 d₂ 1 d₁ + 1 d₂ ]= ₀ A d₁+d₂ & C_ eq = 1 4 9 10^9 36 10⁻⁴ 3 10⁻³+1 10⁻³ & ( 1 4 ₀ =9 10^9 Nm ^2 / C ^2 ) & = 1 4 10⁻¹⁰=25 10⁻¹² ~F =25 pF aligned So, the correct option is (3).