Define capacitance of capacitor. Obtain relation for equivalent capacitance for capacitors connected in series and parallel.

Capacitance Long Question Solution

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Define capacitance of capacitor. Obtain relation for equivalent capacitance for capacitors connected in series and parallel.

Capacitance - Long Question Answer 2

Question: Define capacitance of a capacitor. Obtain relation for equivalent capacitance for capacitors connected in series and parallel.

Answer: Capacitance of a capacitor defines as the ability of a capacitor to store charge is called its capacitance. The rise in potential difference between conducting plates is directly proportional to the charge given to them i.e. q α V => q = C V

Where C is constant of proportionality called capacitance of a conductor. Thus,

C = q/v

When v = 1volt, then C = q

Thus, capacitance of a capacitor is numerically equal to the charge required to rise P.D. by 1 volt. The SI unit of capacitance is Farad (F).

Series combination of a Capacitor: 

The capacitors are said to be joined in series if the charge on each capacitor is same while voltage across them id different.

series combination of capacitor

Suppose C1 and C2 are the capacitances of two capacitors which are connected to the terminals of a DC cell with P.D. V so that charge on each capacitor is q. The voltages across capacitors are V1 = q/C1 and V2 = q/C2.

Thus, the total voltage across that becomes

V = V1 + V2 = q/C1 + q/C2

V/q = 1/C1 + 1/C                                                                                          

1/C = 1/C1 + 1/C2 Since, C = q/V

Thus, for series combination, the reciprocal of equivalent capacitor is equal to the sum of reciprocal of capacitance of individual capacitor. 

Parallel combination of capacitors:

Parallel combination of capacitor

The capacitors are said to be in parallel combination If each capacitor is directly connected to a source So that voltage across each capacitor remains same while the charge is different. 

Suppose C1 and C2 are the capacitance of two capacitors, which are joined in parallel across a source of emf V.

Suppose C is the P.D. between the plates of each capacitor, then charge on each capacitor is q1 = C1V and q2 = C2V respectively.

Thus, the total charge becomes,

Q = q1 + q2

Q =C1V + C2V

Q = V (C1 + C2)

Q/V = C1 + C2

C = C1 + C2 Since, Q/V = C

Hence, the total capacitance of a capacitor in parallel combination is the sum of individual capacitance of capacitors.

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