Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
Share

# P Three Capacitors Having Capacitances 20 µF, 30 µF and 40 µF Are Connected in Series with a 12 V Battery. Find the Charge on Each of the Capacitors. How Much Work Has Been Done - Physics

ConceptCapacitors and Capacitance

#### Question

Three capacitors having capacitances 20 µF, 30 µF and 40 µF are connected in series with a 12 V battery. Find the charge on each of the capacitors. How much work has been done by the battery in charging the capacitors?

#### Solution

When the capacitors are connected in series, the equivalent capacitance is given by 1/C_(eq) = 1/C_1 + 1/C_2 + 1/C_3

1/C_(eq) = (1/20 + 1/30 + 1/40) xx 1/10^-6

⇒ C_(eq) = 9.23  "uF"

Because the capacitors are connected in series, the same charge will go to each of them and it is equal to the total charge given by the battery.
Now,
Let the charge at each capacitor be q.

therefore q = CV = (9.23 xx 10^-6) xx 12

q = 110.76   "uC"

The Work done by the battery (W) is given by

W = qV

⇒ W = 12 xx 110.76 xx 10^-6

⇒ W = 1.33 xx 10^-3 J

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL 

Solution P Three Capacitors Having Capacitances 20 µF, 30 µF and 40 µF Are Connected in Series with a 12 V Battery. Find the Charge on Each of the Capacitors. How Much Work Has Been Done Concept: Capacitors and Capacitance.
S