Question

In the given arrangement of capacitors equivalent capacitance between points M and N is 

(A) (5 / 4)c 

(B) (4 / 5)c 

(C) (4 / 3)c 

(D) (3 / 4)c

Answer 1

The correct option (A) (5/4)c   

Explanation:

The circuit can be drawn as shown. All capacitors have value c from diagram, c₁ & c₂ are in series

∴ equivalent = [(1/c) + (1/c)]^–1 = (c/2)

This (c/2) & c₃ are in parallel

hence equivalent = (c/2) + c = (3/2)c

Also c_4­ & c₅ are in series, their equivalent is

[(1/c) + (1/c)]^–1 = (c/2)

hence it can be redrawn as

For upper half & lower half of circuit, c, c, (3c/2) are in series

∴ Equivalent = [1/{(1/c) + (1/c) + (2/3c)] = (3c/8)

hence (3c/8), (c/2), (3c/8) are in parallel

hence final equivalent capacitance is

= (3c/8) + (3c/8) + (c/2)

= [(3c + 3c + 4c)/8]

= [(10c)/8] = (5c/4)