Answer:
value of L = 4.75 cm
Explanation:
given data
capacitor = 100 pF = 100 × [tex]10^{-12}[/tex] F
thick = 0.20 mm = 2 × [tex]10^{-4}[/tex] m
solution
we get here area of each plate that is
area = L² .......................1
and
Capacitance, C = εo A ÷ d ..................2
put here value so we get
100 × [tex]10^{-12}[/tex] = 8.854 × [tex]10^{-12}[/tex] × L² ÷ ( 2 × [tex]10^{-4}[/tex] )
solve it and we will get
L = 0.047528 m
value of L = 4.75 cm
The length of the square metal inserted between the corners is 47.5 mm.
The capacitance of capacitor is determined by taking the ratio of area of the capacitor to the diameter of the capacitor as follows;
[tex]C = \frac{\varepsilon _o A}{d} \\\\C = \frac{\varepsilon _o L^2}{d}\\\\L^2 = \frac{Cd}{\varepsilon _o} \\\L = \sqrt{ \frac{Cd}{\varepsilon _o}}[/tex]
where;
The length of the square metal inserted between the corners is calculated as follows;
[tex]L = \sqrt{ \frac{100 \times 10^{-12} \times 0.2 \times 10^{-3}}{8.85 \times 10^{-12} }} \\\\L= 0.0475 \ m\\\\L = 47.5 \ mm[/tex]
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