Question

Find the equivalent capacitance between points A and B:

$\begin{aligned} & \text{A}\text{. }\dfrac{5C}{3} \\\ & \text{B}\text{. }\dfrac{4C}{3} \\\ & \text{C}\text{. 2C} \\\ & \text{D}\text{. C} \\\ \end{aligned}$

Answer 1

Find the mathematical expression for the total capacitance of a circuit with capacitors connected in parallel and capacitors connected in series. First simplify the given circuit to find out if the capacitors are connected in series or parallel. Then solve the circuit accordingly.

Complete step by step answer:
A capacitor is an electronic device which stores electrical energy inside an electric field. The capacitor stores energy in the form of electrical charge which produces a potential difference between the two plates of the capacitor. It is a passive electrical component.
If two capacitors ${{C}_{1}}$ and ${{C}_{2}}$ are connected in series to each other the total capacitance of the system is given as,
$\dfrac{1}{C}=\dfrac{1}{{{C}_{1}}}+\dfrac{1}{{{C}_{2}}}$
If two capacitors ${{C}_{1}}$ and ${{C}_{2}}$ are connected in parallel to each other the total capacitance of the system is given as,
$C={{C}_{1}}+{{C}_{2}}$
Now, simplifying the given circuit in the question we can draw,

The total capacitance of the two parallel capacitors with capacitance C each,
$C+C=2C$

Now, the capacitor with capacitance C and 2C are connected in series with each other. The total capacitance will be,
$\begin{aligned} & \dfrac{1}{{{C}_{1}}}=\dfrac{1}{C}+\dfrac{1}{2C}=\dfrac{3}{2C} \\\ & {{C}_{1}}=\dfrac{2}{3}C \\\ \end{aligned}$

These two capacitors are connected in parallel to each other. So, the total capacitance will be,
$C+\dfrac{2}{3}C=\dfrac{5}{3}C$

So, the total capacitance between the points A and B is $\dfrac{5}{3}C$.

So, the correct answer is “Option A”.

Note: Capacitance of a capacitor can be defined as the ability of the capacitor to store energy in the form of the electrical charge. It is the ratio of the change in electric charge to the corresponding change in electric potential of the capacitor. The SI unit of the capacitance is Farad.