Find the charges on the three capacitors connected to a battery as shown in figure (31-E1) Take $C_{1} = 2 \cdot 0 μ F, C_{2} = 4 \cdot 0 μ F, C_{3} = 6 \cdot 0 μ F and V = 12 volts .$

Open in App

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
C_eq = C₁ + C₂ + C₃
= (2 + 4 + 6) μF = 12 μF = 12 × 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

Q₁= C₁V = (2 × 10^{$-$ 6}) × 12 C = 24 × 10^{$-$ 6} C = 24 μC

Similarly, the charges on the other two capacitors are given by
Q₂= C₂V = (4 × 10^{$-$ 6}) × 12 C = 48 × 10^{$-$ 6} C = 48 μC
and
Q₃= C₃V = (6 × 10^{$-$ 6}) × 12 C = 72 × 10^{$-$ 6} C = 72 μC

Suggest Corrections

Similar questions

Find the charges on the three capacitors connected to a battery as shown in figure (31-E1). Take $C_{1} = 2.0 μ F, C_{2} = 4.0 μ F, C_{3} = 6.0 μ F$ and $V = 12$ volts.

Q. Take

C_{1} = 4 \cdot 0 μ F and C_{2} = 6 \cdot 0 μ F

in figure (31-E3). Calculate the equivalent capacitance of the combination between the points indicated.

Q. Two capacitors of capacitances 4⋅0 µF and 6⋅0 µF are connected in series with a battery of 20 V. Find the energy supplied by the battery.

Q. Three capacitors

C_{1}, C_{2}

and

C_{3}

are connected to a battery of

6 V

as shown in figure. Find the charges on the three capacitors.

Q. Three capacitors

C_{1}

C_{2}

and

C_{3}

are connected as shown in the figure to a battery of V volt. If the capacitor

C_{3}

breaks down electrically the change in total charge on the combination of capacitors is:

Join BYJU'S Learning Program

Find the charges on the three capacitors connected to a battery as shown in figure (31-E1) Take C1=2·0 μF, C2=4·0 μF, C3=6·0 μF and V=12 volts.

Find the charges on the three capacitors connected to a battery as shown in figure (31-E1) Take $C_{1} = 2 \cdot 0 μ F, C_{2} = 4 \cdot 0 μ F, C_{3} = 6 \cdot 0 μ F and V = 12 volts .$