Question

Find equivalent capacitance between points A and B. Assume each conducting plate has same dimensions and neglect the thickness of plate. It is given that \[ \frac{6A\varepsilon_0}{d}=7\,\mu F, \] where A is the area of plates.

• A. 7 \mu F
• B. 11 \mu F
• C. 12 \mu F
• D. 15 \mu F

Hint:

Capacitance of parallel gaps simply adds when connected across same points.

Answer 1

The Correct Option is C

Step 1: From the figure, there are three capacitors formed by six plates. For plates of equal area, capacitances are proportional to \( \frac{A\varepsilon_0}{\text{separation}} \).
Step 2: Using the given reference: \[ \frac{6A\varepsilon_0}{d}=7\,\mu F \Rightarrow \frac{A\varepsilon_0}{d}=\frac{7}{6}\,\mu F. \]
Step 3: The three gaps in the diagram are \(d,\;d,\;2d\). Therefore individual capacitances: \[ C_1=C_2=\frac{7}{6}\,\mu F,\qquad C_3=\frac{7}{12}\,\mu F. \]
Step 4: These are in parallel between A and B: \[ C_{\text{eq}}=C_1+C_2+C_3 =\frac76+\frac76+\frac7{12} =\frac{14}{6}+\frac7{12} =\frac{28+7}{12} =\frac{35}{12}\times4 =12\,\mu F. \] Hence → (C).