Name: Dielectrics in a Capacitor
Uploaded: 2019-07-19
Duration: 6 min 3 s
Description: Let us use our knowledge about dielectrics and capacitors to find out how the use of dielectrics can increase the capacitance of a system. Learn through this...

Question

Explain series combination and parallel combination of condensers with circuit diagram and obtain expressions for equivalent of both type of combinations.

Accepted Answer

Capacitors can be arranged as series and parallel in two simple and common relation forms for which the overall capacitance can be easily measured. The series and parallel of these two simple variations can be used even as part of complex relations. The reciprocal number of the equivalent capacitance is the sum of the reciprocal capacities of each capacitor in a series combination.

As for every capacitor, it relies on load and voltage by means of the capacitance of the mixture. Each capacitor acquires the same charge Q when the series combination is attached to a battery with voltage V. Firstly, the battery's positive terminal charge is +Q and the negative terminal charge is −Q. To illustrate, it cannot be skipped on the plate. Charges on the other plates are then caused to zero on all plates except for every pair of capacitor plates. The number of charges is 0. The potential drop $V = \frac{Q}{C_{1}}$ on one capacitor could be different, as the capacitor normally has different capacities, from the potential drop $V = \frac{Q}{C_{2}}$ on another condenser. The two or three-condenser combination series looks like a single capacitor with less power

Now, as given in the figure, consider three capacitors $C_{1}, C_{2}$ and $C_{3}$ are connected in series combination,
Now, the charge on first capacitor would be, $Q_{1} = C_{1} V_{1}$
The charge on second capacitor would be, $Q_{2} = C_{2} V_{2}$
The charge on third capacitor would be, $Q_{3} = C_{3} V_{3}$
In series combination, all the charges are equal, or,

$Q_{1} = Q_{2} = Q_{3} = Q$

Also, the total voltage will be,

$V = V_{1} + V_{2} + V_{3}$

Therefore,

$Q = C_{eq} V$

on writing above equation in terms of voltage, we have

$V = \frac{Q}{C_{Eq}}$

$\frac{Q}{C_{Eq}} = \frac{Q}{C_{1}} + \frac{Q}{C_{2}} + \frac{Q}{C_{3}}$

$\frac{1}{C_{Eq}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}}$

The expression for equivalent capacitance in series combination is

. $\frac{1}{C_{Eq}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}}$ .

Parallel combination of capacitors

Figure below shows two capacitors connected in parallel between two points A and B

Right hand side plate of capacitors would be at same common potential V_A.Similarly left hand side plates of capacitors would also be at same common potential V_B.

Thus in this case potential difference $V_{AB} = V_{A} - V_{B}$ would be same for both the capacitors, and charges Q₁ and Q₂ on both the capacitors are not necessarily equal. So,
Q₁=C₁V and Q₂=C₂V

Thus charge stored is divided amongst both the capacitors in direct proportion to their capacitance.

Total charge on both the capacitors is,
Q=Q₁+Q₂
=V(C₁+C₂)
and
Q/V=C₁+C₂
So system is equivalent to a single capacitor of capacitance
C=Q/V
where,

When capacitors are connected in parallel their resultant capacitance C is the sum of their individual capacitances.

The value of equivalent capacitance of system is greater then the greatest individual one.

If there are number of capacitors connected in parallel then their equivalent capacitance would be
C=C₁+C₂+ C₃...........

this is the formula for equivalent capacitance in parallel.

Explain series combination and parallel combination of condensers with circuit diagram and obtain expressions for equivalent of both type of combinations.

Important Questions on Electrostatic Potential and Capacitance

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