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Find the Charges on the Three Capacitors Connected to a Battery as Shown in Figure Take C 1 = 2.0 U F , C 2 = 4.0 U F , C 3 = 6.0 U F and V = 12 Volts . - Physics

Sum

Find the charges on the three capacitors connected to a battery as shown in figure.

Take `C_1 = 2.0  uF , C_2 = 4.0  uF , C_3 = 6.0  uF and V` = 12 volts.

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Solution

The capacitances of three capacitors are C1= 2 μF, C2= 4 μF and C3= 6 μF and the voltage of the battery (V) is 12 V.

As the capacitors are connected in parallel, the equivalent capacitance is given by
Ceq = C1 + C2 + C3

= `(2+4+6)  uF = 12  uF = 12 xx 10^-6 "F"`

Due to parallel connection, the potential difference across each capacitor is the same and is equal to 12 V.

Therefore, the charge on each capacitor can be calculated as follows :
The charge on the capacitor of capacitance C1= 2 μF is given by

`Q_1 = C_1V = (2 xx 10^-6) xx 12  "C" = 24 xx 10^-6  "C" = 24  "uC"`

Similarly, the charges on the other two capacitors are given by 

`Q_2 = C_2V = (4 xx 10^-6) xx 12  "C" = 48 xx 10^-6  "C" = 48  "uC"`

and 

`Q_3 = C_3V = (6 xx 10^-6) xx 12  "C" = 72 xx 10^-6  "C" = 72  "uC"`

Concept: Capacitors and Capacitance
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 9 Capacitors
Q 6 | Page 165
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