Reducing Capacitor Networks

Work from the inside out

Worked example

A mixed network

A 45 μF capacitor is in series with a parallel pair of 10 μF and 20 μF. Find the combined capacitance.

Combine the parallel pair.
$C_{\parallel}=10+20=30\ \mu\mathrm{F}$
Combine 45 μF and 30 μF in series.
$\dfrac{1}{C_{\mathrm T}}=\dfrac{1}{45}+\dfrac{1}{30}$

Answer

C_{\mathrm T}=18\ \mu\mathrm{F}

Your turnquick check

One capacitor C is in parallel with two identical capacitors C in series. Express the combined capacitance in terms of C.

Show worked answer

C_{\mathrm{series}}=\dfrac{C}{2}

Answer

C_{\mathrm T}=C+\dfrac{C}{2}=\dfrac{3C}{2}

Worked example

A mixed network

A 45 μF capacitor is in series with a parallel pair of 10 μF and 20 μF. Find the combined capacitance.

Combine the parallel pair.
$C_{\parallel}=10+20=30\ \mu\mathrm{F}$
Combine 45 μF and 30 μF in series.
$\dfrac{1}{C_{\mathrm T}}=\dfrac{1}{45}+\dfrac{1}{30}$

Answer

C_{\mathrm T}=18\ \mu\mathrm{F}

Your turnquick check

One capacitor C is in parallel with two identical capacitors C in series. Express the combined capacitance in terms of C.

Show worked answer

C_{\mathrm{series}}=\dfrac{C}{2}

Answer

C_{\mathrm T}=C+\dfrac{C}{2}=\dfrac{3C}{2}