question_answer

Find the effective capacitance between P and Q in  the given figure:

A)  C                                                           

B)  4 C

C)  2 C                                        

D)  C/2

Correct Answer: A

Solution :

 It is based on the Wheat stone bridge, so in the middle branch the capacitance is ineffective. In the upper arms capacitance are connected in the series. Hence, its equivalent capacitance is given by \[{{\text{C}}_{{{\text{s}}_{1}}}}=\frac{C\times C}{C+C}=\frac{C}{2}\] Similarly, in lower arms the equivalent capacitance is given by \[{{\text{C}}_{{{\text{s}}_{2}}}}=\frac{C\times C}{C+C}=\frac{C}{2}\] Now, the \[{{C}_{{{s}_{1}}}}\]and \[{{C}_{{{s}_{2}}}}\]are parallel. Hence,   their   equivalent   capacitance between P and Q is given by \[{{C}_{PQ}}=\frac{C}{2}+\frac{C}{2}=C\]