Question

The effective capacitance between the points P and Q in the circuit shown in figure, is (capacitance of each capacitor is $ 1\mu F $ ):

• A. $ 0.4\mu F $
• B. $ 3\mu F $
• C. $ 4\mu F $
• D. $ 2\mu F $

Answer 1

Answer: (A)

The circuit diagram is shown in figure

As shown, $ {{C}_{3}} $ and $ {{C}_{4}} $ are in parallel, hence their effective capacitance is
$ C={{C}_{3}}+{{C}_{4}}=1+1=2\mu F $
Now $ {{C}_{1}},{{C}_{2}} $ and $ C $ are in series, hence their effective capacitance is

$ \frac{1}{C}=\frac{1}{{{C}_{1}}}+\frac{1}{C}+\frac{1}{{{C}_{2}}} $
$ =\frac{1}{1}+\frac{1}{2}+\frac{1}{1} $
$ =2+\frac{1}{2}=\frac{5}{2} $
$ \therefore $ $ C=\frac{2}{5}=0.4\,\mu F $