Three parallel-plate capacitors are constructed, each havingthe same plate area A and with C1 having plate spacing d1,C2 having plate spacing d2, and C3 having plate spacing d3.Show that the total capacitance C of the three capacitors connectedin series is the same as a capacitor of plate area A andwith plate spacing d = d1 +d2 x d3.

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Asked Dec 18, 2019
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Three parallel-plate capacitors are constructed, each having
the same plate area A and with C1 having plate spacing d1,
C2 having plate spacing d2, and C3 having plate spacing d3.
Show that the total capacitance C of the three capacitors connected
in series is the same as a capacitor of plate area A and
with plate spacing d = d1 +d2 x d3.

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Expert Answer

Step 1

The equation for the net capacitance of the series connection is given by,

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C C C, C3 C +C, +. GC, C3 (G +C;)C; + GC, GC,C; CC; +C,C; + GC, GC,C; GC,C; (1) GC, +GC; +C,C3 Here, C is the net capacitance of the series connection. The equation for C, is given by, d Here, ɛ is the absolute permittivity. ||

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Step 2

The equation for C2 is given by,

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E,A C, = d, The equation for C, is given by, C3 dz

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Step 3

Putting the above three equat...

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E,A d , d, d, =- E,A E,4 аалЕ E,A E,A d, dz d, d, d,d,dz вд е4 в4 d,d, d,d, d,d, E,A d;d,d3 d d, d, d,d, 2. d,d,dz d, +d, d,d,dz d,dz

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Science

Physics

Electrostatic Potential and Capacitance

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