Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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A Finite Ladder is Constructed by Connecting Several Sections of 2 µF, 4 µF Capacitor Combinations as Shown in the Figure. - Physics

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Question

A finite ladder is constructed by connecting several sections of 2 µF, 4 µF capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance C. What value should be chosen for C, such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between?

Solution

The equivalent capacitance of the ladder between points A and B becomes independent of the number of sections in between when the capacitance between A and B is C.

The capacitors C and 4 µF are in series; their equivalent capacitance is given by `C_1 = (C xx 4) / (C+4)`

The capacitors C1 and 2 µF are in parallel; their equivalent capacitance is given by C = C1 + 2 µF

`⇒ C = (C xx 4) / (C+4) + 2`

⇒ 4C + 8 + 2 C = 4C + C2

⇒ C2 − 2C − 8 = 0

⇒ C = −2, C = 4

Capacitance cannot be negative.

∴ C = 4 µF

The value of C is 4 µF.

  Is there an error in this question or solution?

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Solution A Finite Ladder is Constructed by Connecting Several Sections of 2 µF, 4 µF Capacitor Combinations as Shown in the Figure. Concept: Capacitors and Capacitance.
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