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Take C 1 = 4.0 Uf and C 2 = 6.0 Uf in Figure . Calculate the Equivalent Capacitance of the Combination Between the Points Indicated. - Physics

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Question

Take `C_1 = 4.0  "uF" and C_2 = 6.0  "uF"` in figure . Calculate the equivalent capacitance of the combination between the points indicated.

Solution

For the combination of capacitors given in figure (a), the pairs of capacitors C1 and C2are in parallel.
The equivalent capacitance of each parallel combination of capacitors is given by
C1 C2 = 4 + 6 = 10 μF
The equivalent circuit can be drawn as :

The  equivalent capacitance for the above series circuit is given by 

`1/C_(eq) = 1/(C_1 + C_2) + 1/(C_1+C_2) = 1/10 + 1/10 = 2/10`

⇒ `C_("eq") = 5  "uF"`

For the combination of capacitors given in figure (b), the pairs of capacitors C1 and C2are in parallel.
The equivalent capacitance of each parallel combination of capacitors is given by
C1 C2 = 4 + 6 = 10 μF

The equivalent circuit can be drawn as : 

In the above circuit, it can be seen that Cand CB are in series and are in parallel to the series combination of Cand CB.

The equivalent capacitance for the series combination of Cand Cis given by

`1/C_(eq) = 1/C_A + 1/C_B = 1/(C_1+C_2) + 1/(C_1 + C_2)= 1/10 + 1/10 = 1/5`

⇒ `C_(eq) = 5  "uF"`

Similarly, the equivalent capacitance of the series combination of Cand Cis 5 μF.

∴ Net equivalent capacitance = 5 + 5 = 10 μF

  Is there an error in this question or solution?

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Solution Take C 1 = 4.0 Uf and C 2 = 6.0 Uf in Figure . Calculate the Equivalent Capacitance of the Combination Between the Points Indicated. Concept: Capacitors and Capacitance.
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