Show that the effective capacitance, C, of a series combination, of three capacitors, $C_{1}, C_{2}$ and $C_{3}$ is given by
$C = \frac{C_{1} C_{2} C_{3}}{(C_{1} C_{2} + C_{2} C_{3} + C_{3} C_{1})}$

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Solution

When the capacitors are in series , the equivalent capacitance, $\frac{1}{C} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}}$
or $\frac{1}{C} = \frac{C_{2} C_{3} + C_{1} C_{3} + C_{1} C_{2}}{C_{1} C_{2} C_{3}}$

or $C = \frac{C_{1} C_{2} C_{3}}{C_{2} C_{3} + C_{1} C_{3} + C_{1} C_{2}}$

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Q. Obtain an expression for equivalent capacitance C, when three capacitors having capacitance

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The equivalent capacitance C for the series combination of three capacitance

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Show that the effective capacitance, C, of a series combination, of three capacitors, C1,C2 and C3 is given byC=C1C2C3(C1C2+C2C3+C3C1)

When the capacitors are in series , the equivalent capacitance, 1C=1C1+1C2+1C3or 1C=C2C3+C1C3+C1C2C1C2C3or C=C1C2C3C2C3+C1C3+C1C2

Show that the effective capacitance, C, of a series combination, of three capacitors, $C_{1}, C_{2}$ and $C_{3}$ is given by
$C = \frac{C_{1} C_{2} C_{3}}{(C_{1} C_{2} + C_{2} C_{3} + C_{3} C_{1})}$

When the capacitors are in series , the equivalent capacitance, $\frac{1}{C} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}}$
or $\frac{1}{C} = \frac{C_{2} C_{3} + C_{1} C_{3} + C_{1} C_{2}}{C_{1} C_{2} C_{3}}$

or $C = \frac{C_{1} C_{2} C_{3}}{C_{2} C_{3} + C_{1} C_{3} + C_{1} C_{2}}$