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Three capacitors each of capacitance 9pF are connected in series as shown in figure.
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(a) What is the total capacitance of the combination?
(b) What is the potential difference across each capacitor, if the combination is connected to a 120volt supply?

Answer
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Hint: To answer the question, we must first determine the capacitance, which we can do by using the formula for determining capacitance when two or more capacitors are connected in series. Summing the reciprocals of the individual capacitances and calculating the reciprocal of the sum can be used to compute the total capacitance of capacitors in series. Then, because the capacitance is equal and connected in series so voltage divides to find voltage across each capacitor.

Complete step by step answer:
It is given to us that three capacitors each of capacitance 9pF are connected in series.Therefore,
C1=C2=C3=9pF=9ร—10โˆ’12F

(a) Since the capacitor are connected in series
1C=1C1+1C2+1C3
Now, putting the values in C1 , C2 and C3
1C=19ร—10โˆ’12+19ร—10โˆ’12+19ร—10โˆ’12
Now, we will take 10โˆ’12 as common
1C=110โˆ’12[19+19+19]
Now we will add up
1C=110โˆ’12ร—39โ‡’1C=110โˆ’12ร—13
โ‡’1C=13ร—10โˆ’12
So, from here the value of C
โˆดC=3ร—10โˆ’12=3pF

Hence, total capacitance of the combination is 3pF.

(b) Potential difference across each capacitor, if the combination is connected to a 120volt supply.It is given to us that combination is connected to a 120volt supply.
Therefore, V=V1+V2+V3
And as the capacitance are equal
 V1=V2=V3=Vโ€ฒ(Let)
Therefore, V=3Vโ€ฒ. Now, from here we will find out the Vโ€ฒ by putting the known values
Vโ€ฒ=V3
Putting the value of V which is given 120volt
โˆดVโ€ฒ=1203=40V(โˆตC1=C2=C3)

Hence, potential difference across each capacitor is 40V.

Note: It's important to note that connecting capacitors in series is done to boost the effective circuit voltage handling capability. Capacitors have a breakdown voltage rating that, if exceeded, increases their risk of failure dramatically. The voltage across two identical capacitors will be divided in half.
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Three capacitors each of capacitance 9pF are connected in series as shown in figure.
seo images

(a) What is the total capacitance of the combination?
(b) What is the potential difference across each capacitor, if the combination is connected to a 120volt supply?

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Electrostatic Potential and Capacitance Class 12 Physics - NCERT EXERCISE 2.6| Vishal Kumar Sir
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