Question

A 0.5 μF and a 11 μF capacitors are connected in series. Then the pair are connected in parallel with a 1.5 μF capacitor. What is the equivalent capacitance? Give answer in terms of mF.

Answer 1

Answer:

$C_{eq}=1.97\ \mu F$

Explanation:

Given that,

Capacitance 1, $C_1=0.5\ \mu F$

Capacitance 2, $C_2=11\ \mu F$

Capacitance 3, $C_3=1.5\ \mu F$

C₁ and C₂ are connected in series. Their equivalent is given by :

$\dfrac{1}{C'}=\dfrac{1}{C_1}+\dfrac{1}{C_2}$

$\dfrac{1}{C'}=\dfrac{1}{0.5}+\dfrac{1}{11}$

$C'=0.47\ \mu F$

Now C' and C₃ are connected in parallel. So, the final equivalent capacitance is given by :

$C_{eq}=C'+C_3$

$C_{eq}=0.47+1.5$

$C_{eq}=1.97\ \mu F$

So, the equivalent capacitance of the combination is 1.97 micro farad. Hence, this is the required solution.