Question:
The equivalent capacitance of the system shown in the figure between the points A and B is:
The equivalent capacitance of the system shown in the figure between the points A and B is:
Show Hint
In symmetric capacitor networks, check for equipotential points to eliminate central components.
Updated On: Jul 18, 2026
- 5 μF
- 10 μF
- 20 μF
- 40 μF
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding circuit symmetry.
The given circuit has two identical branches (top and bottom) with 10 μF capacitors and a central 5 μF capacitor connecting the midpoints. The structure is symmetric about the central axis.
Step 2: Identifying equal potentials.
Due to symmetry, the midpoints of top and bottom branches are at equal potential. Therefore, no potential difference exists across the central 5 μF capacitor.
Step 3: Eliminating central capacitor effect.
Since potential difference across 5 μF capacitor is zero: \[ Q = CV = 0 \] So it does not affect equivalent capacitance.
Step 4: Simplifying each branch.
Each branch has two 10 μF capacitors in series: \[ C_{series} = \frac{10 \times 10}{10 + 10} = 5 \, \mu F \] So each branch becomes 5 μF.
Step 5: Combining parallel branches.
Now two 5 μF branches are in parallel: \[ C_{eq} = 5 + 5 = 10 \, \mu F \]
Step 6: Final conclusion.
\[ \boxed{10 \, \mu F} \]
The given circuit has two identical branches (top and bottom) with 10 μF capacitors and a central 5 μF capacitor connecting the midpoints. The structure is symmetric about the central axis.
Step 2: Identifying equal potentials.
Due to symmetry, the midpoints of top and bottom branches are at equal potential. Therefore, no potential difference exists across the central 5 μF capacitor.
Step 3: Eliminating central capacitor effect.
Since potential difference across 5 μF capacitor is zero: \[ Q = CV = 0 \] So it does not affect equivalent capacitance.
Step 4: Simplifying each branch.
Each branch has two 10 μF capacitors in series: \[ C_{series} = \frac{10 \times 10}{10 + 10} = 5 \, \mu F \] So each branch becomes 5 μF.
Step 5: Combining parallel branches.
Now two 5 μF branches are in parallel: \[ C_{eq} = 5 + 5 = 10 \, \mu F \]
Step 6: Final conclusion.
\[ \boxed{10 \, \mu F} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Capacitance Questions
- When a parallel plate capacitor is charged up to 95 V, its capacitance is \( C \). If a dielectric slab of thickness 2 mm is inserted between plates and the plate separation is increased by 1.6 mm such that the potential difference remains constant, find the dielectric constant of the material:
Four metal plates, each with surfa area $A$ on one side, are plad with separation $d$ as shown in the figure. The capacitan between a and b is ($\varepsilon_0$ -- permittivity of free spa)
- Between the plates of a parallel plate capacitor of plate area A and capacity 0.025 \( \mu \)F, a metal plate of area A and thickness equal to \( \frac{1}{3} \) of the separation between the plates of the capacitor is introduced. If the capacitor is charged to 100 V, then the amount of work done to remove the metal plate from the capacitor is
- A capacitor of capacitance 2 μF is charged with the help of a 60 V battery. After disconnecting the battery, if this capacitor is connected in parallel with another uncharged capacitor of capacitance 1 μF, then the potential difference across the plates of the 2 μF capacitor is
- In the given circuit, the internal resistance of the cell is zero. If \( i_1 \) and \( i_2 \) are the readings of the ammeter when the key (K) is opened and closed respectively, then \( i_1 : i_2 = \)
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions