Parallel Connected Capacitors are connected in parallel when both terminals are connected to each terminal of another capacitor.
All connected in parallelthe voltage of capacitors (Vc)is the same, the capacitors in parallel have a "common voltage" source, which provides the following between them:
VC1 = VC2 = VC3 = VAB = 12V
In the following circuitcapacitors are connected on a parallel branch between all points C1, C2 and C3. When capacitors are connected to each other, the total or equivalent capacitance is collected in the parallel CT circuit.
Since capacitance is related to plate C area (C = ε(A/d), the capacitance value of the combination will also increase.Then the total capacitance value of parallel connected capacitors is actually calculated by collecting the plate area.In other words, the total capacitance is equal to the sum of all individual capacitances in parallel.Parallelyou may have noticed that the total capacitance of capacitors is found in the same way as the total resistance of serial resistors.
Eachit is related to currents passing through the capacitor and voltage, as we saw in the previous lesson.Then we can apply Kirchoff's Current Law (KCL) to the above circuit to obtain the following equations:
and this can be rewritten as follows:
Then we can define the total or equivalent circuit capacitance, C T gives us the generalized equation as the sum of the sum of all individual capacitances:
Parallel Capacitors Equation
When adding capacitors in parallel, they should all be converted into the same capacitance units, whether μF, nF or pF.In addition, we can see that the current passing through the total capacitance value is the same as CT , total circuit current, IT.
At the same time, we can define the total capacitance of the parallel circuit from the total stored Coulomb load using the Q = CV equation for the load on a capacitor plates.The total Q load stored on all platesequals the sum of individual loads stored in the capacitor, therefore:
Since voltage ( V) is common to parallel connected capacitors, we can divide both sides of the above equation only by the voltage separated from the capacitance, and it simply collects the value of the individual capacitances, giving the total capacitance, C T .Also, this equation does not depend on the number of Parallel Capacitors in the branch, and therefore can be generalized for any number of interconnected N parallel capacitors.
Parallel Connected Capacitors Question Example 1
Therefore, by taking the values of the three capacitors from the example above, we can calculate the total equivalent circuit capacitance C T as follows:
CT = C1 + C2 + C3 = 0.1uf + 0.2uF + 0.3uF = 0.6uF
An important point to remember about parallel connected capacitor circuits is that the total capacitance (C T) of any two or more capacitors connected parallel to each other will always be GREATER than the value of the largest capacitor in the group when collecting values.So in the example above, the greater value of T = 0.6μF is only 0.3μF if the capacitor is .
When a larger number of capacitors are connected together to the total capacity of the circuit 4, 5, 6 or C-T will still be the total that is added to the individual capacitors each other and now we know that a parallel circuit should have a higher total capacity than the highest value capacitor.
This is because we have effectively increased the total surface area of the plates.If we do this with two identical capacitors, we have doubled the surface area of the plates, which has doubled the capacitance of the combination, etc.
Parallel Connected Capacitors Question Example 2
When the following capacitors are connected in a parallel combination, calculate the combined capacitance in micro-Farad (μF):
- a) two capacitors, each with a capacitance of 47nF
- b) A 470nF capacitor connected parallel to a 1μF capacitor
a) Total Capacity,
CT = C1 + C2 = 47nF + 47nF = 94nF or 0.094μF
b) Total Capacity,
CT = C1 + C2 = 470nF + 1μF
therefore, CT = 470nF + 1000nF = 1470nF or 1.47μF
Therefore, the total or equivalent capacitance of an electrical circuit containing two or more capacitors in parallel, CT, is the sum of all individual capacitances added together as the active area of the plates increases.
In our next tutorial on capacitors, we will look at connecting Serial Connected Capacitors and the effect of this combination on total capacitance, voltage and current.