Answer to Question #113135 in Electric Circuits for James

Question

Two 6µF capacitance are connected in series with one having a capacitance of 12µF.Find the total equivalent circuit capacitance. What capacitance must be added in series to obtain a capacitance of 1.2µF.

Answer 1

Explanations

• The equivalent capacitance of a set of capacitors connected in series is given by

$\qquad\qquad \small \frac{1}{C_{eq}} = \small \frac{1}{C_1}+ \frac{1}{C_2}+ \frac{1}{C_3} + \cdots\\$

• Equivalent of a set connected in parallel is given by

$\qquad\qquad \small C_{eq} = \small C_1 + C_2 + C_3 + \cdots$

Calculations

1) Since all the capacitors are connected in series,

$\qquad \begin{aligned} \small \frac{1}{C_{eq}} &= \small \frac{1}{6\mu F}+ \frac{1}{6\mu F}+ \frac{1}{12\mu F} \\ \small C_{eq} &= \small \bold{2.4\mu F} \end{aligned}$

2)

If the needed capacitance is C then,

$\qquad \begin{aligned} \small \frac{1}{1.2} &= \small \frac{1}{2.4\mu F}+ \frac{1}{C}\\ \small C &= \small \bold{2.4\mu F} \end{aligned}$