Capacitor in parallel

CAPACITOR IN PARALLEL -

Capacitors are connected together in parallel when both of its terminals are connected to each terminal of another capacitor.

→ When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitors’ capacitances. If two or more capacitors are connected in parallel, the overall effect is that of a single equivalent capacitor having the sum total of the plate areas of the individual capacitors. As we’ve just seen, an increase in plate area, with all other factors unchanged, results in increased capacitance.

→In the following circuit the capacitors, C1, and C2 are all connected together in a parallel branch as shown fig 1.1

FIG. 1.1

→In order to obtain the equivalent capacitor of three capacitors in parallel, consider the circuit in fig. 1.1. The equivalent circuit is in fig. 1.2.

→Note that the capacitors have the same voltage v across them.

→Applying KCL to fig. 1.1

Then we can define the total or equivalent circuit capacitance, CT as being the sum of all the individual capacitance’s add together giving us the generalized equation of:

Parallel Capacitors Equation For N Capacitor -

When adding together capacitors in parallel, they must all be converted to the same capacitance units, whether it is μF, nF or pF. Also, we can see that the current flowing through the total capacitance value, CT is the same as the total circuit current, iT

We can also define the total capacitance of the parallel circuit from the total stored coulomb charge using the Q = CV equation for a charge on the plates of a capacitor. The total charge QT stored on all the plates equals the sum of the individual stored charges on each capacitor, therefore,

As the voltage, ( V ) is common for parallel-connected capacitors, we can divide both sides of the above equation through by the voltage leaving just the capacitance and by simply adding together the value of the individual capacitances gives the total capacitance, CT. Also, this equation is not dependent upon the number of Capacitors in Parallel in the branch, and can, therefore, be generalized for any number of N parallel capacitors connected together.

↳ Note that capacitors in parallel combine in the same manner as resistors in series.

EXAMPLE NO 1 -

Find the equivalent capacitance seen between terminals a and b of the circuit in fig. 2.1.

FIG. 2.1

SOLUTION -

The capacitor 10μF and 7 μFare in parallel; their equivalent capacitor is

10+7 = 17 μF

EXAMPLE NO 2 -

Find the equivalent capacitance seen between terminals a and b of the circuit in fig. 2.2.

FIG. 2.2

SOLUTION -

The capacitor 30μF, 40μF and 70μF are in parallel; their equivalent capacitor is

30+40+70 = 140μF

EXAMPLE NO 3 -

Calculate the combined capacitance in micro-Farads (μF) of the following capacitors when they are connected together in a parallel combination:

a) two capacitors each with a capacitance of 40nF
b) one capacitor of 300nF connected in parallel to a capacitor of 1μF

SOLUTION -

a) Total Capacitance,

CT = C1 + C2 = 40nF + 40nF = 94nF or 0.080μF

b) Total Capacitance,

CT = C1 + C2 = 300nF + 1μF

therefore, CT = 300nF + 1000nF = 1300nF or 1.300μF

So, the total or equivalent capacitance, CT of an electrical circuit containing two or more Capacitors in Parallel is the sum of the all the individual capacitance’s added together as the effective area of the plates is increased.

Introduction of capacitor -

https://educatdeck.blogspot.com/capacitor.html

Capacitor Types - https://educatdeck.blogspot.com/capacitor-types.html

Capacitor in parallel