First slide

Capacitance

Question

Given a number of capacitors labelled as C, V. Find the minimum number of capacitors needed to get an arrangement equivalent to C_net, V_net

Difficult

A

$n = \frac{C_{net}}{C} x \frac{{V_{net}}^{2}}{V^{2}}$
B

$n = \frac{C}{C_{net}} x \frac{V^{2}}{{V_{net}}^{2}}$
C

$n = \frac{C}{C_{net}} x \frac{V}{V_{net}}$
D

$n = \frac{C_{net}}{C} x \frac{V_{net}}{V}$

Solution

n in series ; m in parallel
$n = \frac{V_{net}}{V} \Rightarrow V_{net} = Vn$
Effective capacitance of chain = C/n
$C_{net} = m \frac{C}{n} \Rightarrow \frac{C_{net}}{C} = \frac{m}{n}$
Total capacitors nm = $\frac{C_{net}}{C} x n x n$
$= \frac{C_{net}}{C} x {[\frac{V_{net}}{V}]}^{2}$

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