Question

3capacitor each of value 2uF are given in how many ways you can connect them and find their effective capacitance in each case​

Answer 1

Answer:

Four ways.

Explanation:

There are four ways in which we can connect the given capacitors:-

1.) All three connected in parallel.

     The net effective capacitance will be C1+C2+C3

            i.e. C = 2+2+2 = 6μF

2.) All three connected in series.

       The net effective capacitance would be

                  $\frac{1}{C} = \frac{1}{C1} + \frac{1}{C2} + \frac{1}{C3}$

                   $\frac{1}{C} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2}$

                   $\frac{1}{C} = \frac{3}{2}$

                  $\ C = \frac{2}{3}$

                  $\ C = 0.66μF$

3.) Two in series and this combination in parallel with third one.

          The net effective capacitance would be

                $\frac{1}{C'} = \frac{1}{C1} + \frac{1}{C2}$

                $\frac{1}{C'} = \frac{1}{2} + \frac{1}{2}$

                $\frac{1}{C'} = \frac{1}{1}$

                 $C' = 1μF$

                 $C = 1 +2$

                 $C = 3μF$

4.) Two in parallel and this combination in series with third one.

           The net effective capacitance would be

                $C' = C1+C2$

                 $C' = 2+2$

                 $C' = 4μF$

                $\frac{1}{C} = \frac{1}{4} + \frac{1}{2}$

                 $\frac{1}{C} = \frac{3}{4}$

                 $C = \frac{4}{3}$

                $C = 1.33μF$

Thanks!

Answer 2

Answer:

These 3 capacitors can be connected in four ways.

Explanation:

Let C1, C2 & C3 be the three capacitors.

Case I : All three capacitors connected in series.

Effective capacitance is,

1/C = 1/C1 + 1/C2 + 1/C3

=> 1/C = 1/2 + 1/2 + 1/2

=> 1/C = 3/2

=> C = 2/3

=> C = 0.66 uF

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Case II : All three capacitors connected in parallel.

Effective capacitance is,

C = C1 + C2 + C2

=> C = 2 + 2 + 2

=> C = 6 uF

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Case III : Two capacitors in series and this combination in parallel with third one.

for series combination of 2 capacitors :

1/C' = 1/C1 + 1/C2

1/C' = 1/2 + 1/2

1/C' = 1 uF

Now,

C' in parallel combination with third capacitor C3

Effective Capacitance is,

C = C' + C3

=> C = 1 + 2

=> C = 3 uF

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Case IV : Two capacitors in parallel and this combination in series with third one.

for parallel combination of 2 capacitors :

C" = C1 + C2

=> C" = 2 + 2

=> C" = 4 uF

Now,

C" in series combination with third capacitor C3

Effective capacitance is,

1/C = 1/C" + 1/C3

=> 1/C = 1/4 + 1/2

=> 1/C = 3/4

=> C = 4/3

=> C = 1.33 uF