Advertisements
Advertisements
Question
Two capacitors of unknown capacitances C1 and C2 are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of C1 and C2. Also calculate the charge on each capacitor in parallel combination.
Solution
When the capacitors are connected in parallel,
Equivalent capacitance, CP=C1+C2
The energy stored in the combination of the capacitors, `E_P=1/2C_pV^2`
`=>E_P=1/2(C_1+C_2)(100^2)=0.25J`
⇒(C1+C2)=5×10−5 .....(i)
When the capacitors are connected in series,
Equivalent capacitance, `C_S=(C_1C_2)/(C_1+C_2)`
The energy stored in the combination of the capacitors,
`E_S=1/2C_SV^2`
`=>E_S=1/2(C_1C_2)/(C_1+C_2)(100)^2=0.045J`
`1/2(C_1C_2)/(5xx10^(-5))(100)^2=0.045J`
⇒C1C2=0.045×10−4×5×10−5×2=4.5×10−10
(C1−C2)2=(C1+C2)2−4C1C2
⇒(C1−C2)2=25×10−10−4×4.5×10−10=7×10−10
`=>(C_1-C_2)=sqrt(7xx10^(-10))=2.64xx10^(-5)`
C1−C2=2.64×10−5 .....(ii)
Solving (i) and (ii), we get
C1 = 35 μF and C2 = 15 μF
When the capacitors are connected in parallel, the charge on each of them can be obtained as follows:
Q1=C1V=35×10−6×100=35×10−4 C
Q2=C2V=15×10−6×100=15×10−4 C
APPEARS IN
RELATED QUESTIONS
Deduce an expression for equivalent capacitance C when three capacitors C1, C2 and C3 connected in parallel.
Figure 4 below shows a capacitor C, an inductor L and a resistor R, connected in series
to an a.c. supply of 220 V
Calculate:
1) The resonant frequency of the given CLR circuit.
2) Current flowing through·the circuit.
3) Average power consumed by the circuit.
Each plate of a parallel plate capacitor has a charge q on it. The capacitor is now connected to a batter. Now,
(a) the facing surfaces of the capacitor have equal and opposite charges
(b) the two plates of the capacitor have equal and opposite charges
(c) the battery supplies equal and opposite charges to the two plates
(d) the outer surfaces of the plates have equal charges
A parallel-plate capacitor having plate area 20 cm2 and separation between the plates 1⋅00 mm is connected to a battery of 12⋅0 V. The plates are pulled apart to increase the separation to 2⋅0 mm. (a) Calculate the charge flown through the circuit during the process. (b) How much energy is absorbed by the battery during the process? (c) Calculate the stored energy in the electric field before and after the process. (d) Using the expression for the force between the plates, find the work done by the person pulling the plates apart. (e) Show and justify that no heat is produced during this transfer of charge as the separation is increased.
The figure shows a network of five capacitors connected to a 100 V supply. Calculate the total energy stored in the network.
Capacitors connected in series have ______
The equivalent capacitance of the combination shown in the figure is ______.
In the circuit shown in figure, initially K1 is closed and K2 is open. What are the charges on each capacitors.
Then K1 was opened and K2 was closed (order is important), What will be the charge on each capacitor now? [C = 1µF]
The capacitors, each of 4 µF are to be connected in such a way that the effective capacitance of the combination is 6 µF. This can be achieved by connecting ______.
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. What is the total capacitance of the combination?
