What Is The Equivalent Capacitance

A lot of problems of this type can exist solved by rearranging the excursion into a more user friendly form.

Past symmetry you tin can say $V_{AB}=0$ and and so y'all become $2C$ every bit the equivalent capacitance.

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In that location is a method for solving such network problems which goes back to outset principles and is equivalent the using Kirchhoff's law which are based on the conservation of charge and the conservation of energy.

The offset thing to do is draw the circuit and label it.
In this case I missed out the left hand capacitor because it volition but be in parallel with the equivalent capacitance of the circuit which is left.

Label the charges $+Q_1, -Q_1$ on each of the capacitors and the voltages $V1$ with an arrow to indicate direction of increased potential.
Looking at the diagram the equivalent capacitance of the network will be $\frac{Q_1+Q_2}{V}$ so you lot need to detect $Q_1+Q_2$ in terms of $Five$ and $C$.
For each capacitor there is a relationship of the form $Q_1=CV_1$.

Looking at the charges first noting that the full accuse at each node where only capacitors are connected must be nothing.

$-Q_2+Q_3+Q_5 = 0$ and $Q_3-Q_1+Q_6 = 0$

Adding these ii equations together $\Rightarrow Q_1+Q_2-Q_5-Q_6= 0 \Rightarrow V_1+V_2=V_5+V_6$

Now looking at the voltages:

$Five=V_1+V_6$ and $Five= V_2+V_5$

Adding these ii equations together

$\Rightarrow 2V =V_1+V_2+V_5+V_6 \Rightarrow 2(V_1+V2) \Rightarrow \dfrac {2(Q_1+Q_2)}{C}$

So the equivalent capacitance is $\dfrac{Q_1+Q_2}{5} = \dfrac{CV}{5} = C$

For the whole circuit the equivalent capacitance is $2C$.

What Is The Equivalent Capacitance,

Source: https://physics.stackexchange.com/questions/237521/definition-of-equivalent-capacitance

Posted by: grigsbyseethe.blogspot.com

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