Question

The capacitance between the points \(A\) and \(B\) in the following figure is

• A. \(\frac{3}{8}\,\mu F\)
• B. \(\frac{9}{4}\,\mu F\)
• C. \(\frac{4}{5}\,\mu F\)
• D. \(2\,\mu F\)

Hint:

In a balanced capacitor bridge, the capacitor in the middle branch has zero potential difference across it, so it can be ignored while finding equivalent capacitance.

Answer 1

The Correct Option is B

Step 1: Check the bridge balance condition.
In the bridge network, \[ \frac{1}{2}=\frac{3}{6} \] So, the bridge is balanced.
Therefore, the \(5\,\mu F\) capacitor connected between the upper and lower junctions has no potential difference across it.
Hence, it does not affect the equivalent capacitance.

Step 2: Find equivalent capacitance of upper branch.
The upper branch has \(1\,\mu F\) and \(3\,\mu F\) in series.
So, \[ C_1=\frac{1\times 3}{1+3} \] \[ C_1=\frac{3}{4}\,\mu F \]

Step 3: Find equivalent capacitance of lower branch.
The lower branch has \(2\,\mu F\) and \(6\,\mu F\) in series.
So, \[ C_2=\frac{2\times 6}{2+6} \] \[ C_2=\frac{12}{8} \] \[ C_2=\frac{3}{2}\,\mu F \]

Step 4: Add the parallel capacitances.
The two branches are in parallel between \(A\) and \(B\).
Therefore, \[ C_{\text{eq}}=C_1+C_2 \] \[ C_{\text{eq}}=\frac{3}{4}+\frac{3}{2} \] \[ C_{\text{eq}}=\frac{3}{4}+\frac{6}{4} \] \[ C_{\text{eq}}=\frac{9}{4}\,\mu F \]

Step 5: Final conclusion.
Therefore, \[ \boxed{\frac{9}{4}\,\mu F} \]