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Please, solve 2nd part of this question

Asked by archanajain7219 | 04 Jun, 2022, 11:31: PM

Expert Answer

The given infinite network of capacitors is given in figure 1.

To get the equivalent capacitance across A₁ and B₁ Let us divide the network left of dashed line P and Q .

Infinite network of capacitors left of dashed line P and Q is given in figure 2.

Let C_eq be the capacitance of this infinite network.

In figure 2 , if we divide the network of capacitors at dahed line R and S ,

then right side part after dashed line R and S also a similar infinite network of capacitors that also C_eq .

This is because of infinite connections of capacitors .

Hence in figure 3 , part of network right side of dashed line RS is simply substituted as C_eq

In figure 3, series combination of 6C and C_eq is in parallel to C .

Hence we get

begin mathsize 14px style fraction numerator 6 C space cross times space C subscript e q end subscript over denominator 6 C space plus space C subscript e q end subscript end fraction plus C space equals space C subscript e q end subscript end style

From above expression we get following quadratic equation

begin mathsize 14px style C subscript e q end subscript superscript 2 space minus space C space C subscript e q end subscript space minus space 6 space C squared space equals space 0 end style

Acceptable root of above quadratic equation is , C_eq = 3 C

Hence equivalent capacitance across A₁ and B₁ is 3C

Answered by Thiyagarajan K | 05 Jun, 2022, 12:40: AM

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