As shown in the figure, two parallel plate capacitors having equal plate area of 200 cm 2 are joined in such a way that a ≠ b . The equivalent capacitance of the combination is x ε 0 F . The value of x is _____.

Step-by-step solution

The given data is A = 200 × 10 - 4   m 2 d = 5   × 10 - 3   m The value of a + b = 4 × 10 - 3   m The formula for a parallel plate capacitor is C = ε 0 A D Let the capacitor with gap a be C 1 and capacitor with gap b be C 2 C 1 = ε 0 A a ,   C 2 = ε 0 A b The equivalent capacitance is 1 C e q = a ε 0 A + b ε 0 A ⇒ C e q = ε 0 A a + b It is given that C e q = x ε 0   F So, ε 0 A a + b = x ε 0 ⇒ x = A a + b ⇒ x