JEE MAIN - Physics (2022 - 27th June Evening Shift - No. 23)
A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $${x \over {15}}{{{ \in _0}A} \over b}$$. The value of x is ____________.
_27th_June_Evening_Shift_en_23_1.png)
Answer
23
Explanation
The circuit is equivalent to 3 capacitors in parallel as shown
_27th_June_Evening_Shift_en_23_2.png)
$${C_{eq}} = {{{\varepsilon _0}A} \over b}\left( {1 + {1 \over 3} + {1 \over 5}} \right) = {{23} \over {15}}{{{\varepsilon _0}A} \over b}$$
$$ \Rightarrow x = 23$$
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