Question

i got 3.98 uF

& Determine the capacitance between pauts A and B: ESHTE E Vio Heros value fitores suf and

Answer 1

For capacitors in parallel connection,

Ceg = C1+C2 +C3+

and for capacitors in series connection,

- .. + + Ст Сз C2 Cea

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Capacitors are in series

LF and 4uF

1F 4uF Cs1

1 Cs 1 4 4 4

s1 |Lо

${\color{Red} C_{s1}=0.8\mu F}$

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Capacitors are in series

ВДF and 5uF

3μF5μF C3

8 53 1 3 5 15 3 OO

$C_{s3}=\frac{15}{8}$

${\color{Red} C_{s3}=1.875\mu F}$

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Capacitors $C_{s1}, 2\mu F\ and\ C_{s3}$ are in parallel

$C_{p1}=C_{s1}+2\mu F+C_{s3}$

$C_{p1}=0.8+2+1.875$

${\color{Red} C_{p1}=4.675\mu F}$

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Consider the next branch

Capacitors $6\mu F\ and\ 8\mu F$ are in series

$\frac{1}{C_{s6}}=\frac{1}{6\mu F}+\frac{1}{8\mu F}$

$\frac{1}{C_{s6}}=\frac{1}{6}+\frac{1}{8}=\frac{8+6}{6*8}=\frac{14}{48}$

$C_{s6}=\frac{48}{14}$

${\color{Red} C_{s6}=3.43\mu F}$

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Capacitors $7\mu F\ and\ 10\mu F$ are in series

$\frac{1}{C_{s7}}=\frac{1}{7\mu F}+\frac{1}{10\mu F}$

$\frac{1}{C_{s7}}=\frac{1}{7}+\frac{1}{10}=\frac{10+7}{7*10}=\frac{17}{70}$

$C_{s7}=\frac{70}{17}$

${\color{Red} C_{s7}=4.12\mu F}$

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Capacitors $C_{s6}, 9\mu F\ and\ C_{s7}$ are in parallel

$C_{p2}=C_{s6}+9\mu F+C_{s7}$

$C_{p2}=3.43+9+4.12$

${\color{Red} C_{p2}=16.55\mu F}$

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Capacitors are in series

$\frac{1}{C_{eq}}=\frac{1}{C_{p1}}+\frac{1}{C_{p2}}$

$\frac{1}{C_{eq}}=\frac{1}{4.675\mu F}+\frac{1}{16.55\mu F}$

$\frac{1}{C_{eq}}=\frac{1}{4.675}+\frac{1}{16.55}=\frac{16.55+4.675}{4.675*16.55}=\frac{21.225}{4.675*16.55}$

$C_{eq}=\frac{4.675*16.55}{21.225}$

ANSWER: ${\color{Red} C_{eq}=3.645\mu F}$

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