Grouping of capacitors
This is the topic in which students will learn about grouping of capacitors , which contain series combination and parallel combination of the capacitors .
(Combination) Grouping of capacitors or condensers –
- Capacitors in series – When negative plate of first capacitor is connected with positive of second , negative of second connected to positive of third and so on such combination is called series combination . in another words we can say that, the capacitors are said to be connected in series between two points , when we can proceed from one point to the other only through one path .
As shown in figure three condensers of capacitance C1 , C2 and C3 are connected in series .
Suppose V is the potential difference across the combination . Suppose ‘Q’ charge is given to the left plate of C1 due to induction -Q charge setup on the other plates and =Q on the left plate of capacitor C2 and so on . Let V1, V2 and V3 are the potential difference setup across the capacitors C1 , C2 and C3 respectively . charge across the capacitors are same which is Q . Then V1 = Q/C1 , V2 = Q/C2 . V3 = Q/C3 . So net potential V = V1 + V2 + V3 ;
If CS is the equivalent capacitance of the combination of the capacitors then ,
Q/CS = Q/C1 + Q/C2 + Q/C3
Or , 1/CS = 1/C1+ 1/C2 + 1/C3
If there are n capacitors are connected in series then
1/CS = 1/C1+ 1/C2 + 1/C3 …………………+ 1/Cn
- Capacitors in parallel – The combination of the two or more capacitors are said to be in parallel if positive plates of capacitors are connected at one point and all negative plates at another points as shown in figure .
Let C1 ,C2 , and C 3 are the capacitance of the three capacitors , and V is the potential difference applied across the combination . The potential difference across each capacitor is V the charge on each are Q1 Q2 and Q3 , because their capacitance are different . S o net charge Q = Q1 + Q2 + Q 3
If CP is the equivalent capacitance of the capacitors then CP V = C1 V + C2 V + C3 V
So, Equivalent capacitance CP = C1 + C2 + C3 ;
If there are n capacitors are connected in parallel then
CP = C1 + C2 + C3……………..+ Cn