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GUJCET · Physics · Electrostatic Potential and Capacitance
In the figure area of each plate is A and the distance between consecutive plates is d. What is the effective capacitance between points A and B.
- A \(\frac{2}{3} \frac{A \varepsilon_0}{d}\)
- B \(\frac{3}{2} \frac{A \varepsilon_0}{d}\)
- C \(\frac{ A \varepsilon_0}{d}\)
- D none of the above.
Answer & Solution
Correct Answer
(A) \(\frac{2}{3} \frac{A \varepsilon_0}{d}\)
Step-by-step Solution
Detailed explanation
(A)
equivalent capacitance of parallel connection of \(C _1\) and \(C _2\)
\(C^{\prime}=C_1+C_2=C+C=2 C\)
equivalent capacitance of series
connection
of \(C^{\prime}\) and \(C_3\)
\(\begin{array}{l} C =\frac{ C ^{\prime} C _3}{ C ^{\prime}+ C _3}=\frac{(2 C ) C }{2 C + C } \\ C =\frac{2}{3} C =\frac{2}{3} \frac{A \varepsilon_0}{d}\end{array}\)
equivalent capacitance of parallel connection of \(C _1\) and \(C _2\)
\(C^{\prime}=C_1+C_2=C+C=2 C\)
equivalent capacitance of series
connection
of \(C^{\prime}\) and \(C_3\)
\(\begin{array}{l} C =\frac{ C ^{\prime} C _3}{ C ^{\prime}+ C _3}=\frac{(2 C ) C }{2 C + C } \\ C =\frac{2}{3} C =\frac{2}{3} \frac{A \varepsilon_0}{d}\end{array}\)
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