Question
(II) Suppose three parallel-plate capacitors, whose plates have areas $A_1 , A_2 ,$ and $A_3$ and separations $d_1, d_2,$ and $d_3,$ are connected in parallel. Show, using only Eq. 17-8, that Eq. 19-5 is valid.
Step 1
The charge on a capacitor is given by the product of its capacitance and the potential difference across it. Since the capacitors are connected in parallel, the potential difference across each of them is the same. Therefore, the charges on the capacitors are Show more…
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Suppose three parallel-plate capacitors, whose plates have areas $A_{1}, A_{2},$ and $A_{3}$ and separations $d_{1}, d_{2},$ and $d_{3}$, are connected in parallel. Show, using only Eq. $24-2,$ that Eq. $24-3$ is valid.
(1I) Suppose three parallel-plate capacitors, whose plates have areas $A_{1}, A_{2},$ and $A_{3}$ and separations $d_{1}, d_{2},$ and $d_{3}$ are connected in parallel. Show, using only $\mathrm{Eq} .2,$ that Eq. 3 is valid. $$C=\frac{Q}{V}=\epsilon_{0} \frac{A}{d} \cdot \quad[\text { parallel-plate capacitor }] (2)$$ $$C_{\mathrm{eq}}=C_{1}+C_{2}+C_{3} . \quad \quad \text { [parallell } ] (3)$$
(II) Three conducting plates, each of area $A,$ are connected as shown in Fig. $19-54$ . ( $a$ ) Are the two capacitors formed connected in series or in parallel? (b) Determine $C$ as a function of $d_{1}, d_{2},$ and $A$ . Assume $d_{1}+d_{2}$ is much less than the dimensions of the plates.
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