Question

Two capacitors of capacitance 4 microfarad and 6 microfarad are connected in parallel this combination is then connected in series to third capacitor is the equivalent capacitance of the arrangement is 10 by 3 microfarad the capacitance of the capacitor is

Answer 1

Capacitance of the capacitor =  $\frac{14}{15}$ microfarad

Given:

Two capacitors of capacitance 4 microfarad and 6 microfarad are connected in parallel

This combination is then connected in series to third capacitor.

The equivalent capacitance of the arrangement is $\frac{10}{3}$ microfarad

To find:

Capacitance of the capacitor.

Formula used:

For parallel connection,

$\frac{1}{Equavalant \ capacitance}$ = $\frac{1}{C_1}$ + $\frac{1}{C_2}$

For series connection,

Equavalant capacitance = $C_1 + C_2$

Explanation:

For parallel connection.

$\frac{1}{Equavalant \ capacitance}$ = $\frac{1}{C_1}$ + $\frac{1}{C_2}$

$\frac{1}{Equavalant \ capacitance}$ = $\frac{1}{4}$ + $\frac{1}{6}$

Equavalant capacitance = $\frac{24}{10}$ = $\frac{12}{5}$ microfaranide.

This capacitor is connected with another capacitor with capacitance = $C_3$

And Equavalant capacitance is $\frac{10}{3}$ microfarad

So  $\frac{12}{5}$  + $C_3$ =  $\frac{10}{3}$

             $C_3$ =  $\frac{10}{3}$ -  $\frac{12}{5}$

              $C_3$ = $\frac{50-36}{15}$

               $C_3$ = $\frac{14}{15}$

Capacitance of the capacitor =  $\frac{14}{15}$ microfarad

To learn more...

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Answer 2

14/15 ...capacitance....