Advertisements
Advertisements
प्रश्न
Derive the expression for resultant capacitance, when the capacitor is connected in series.
Advertisements
उत्तर
Consider three capacitors of capacitance C1, C2 and C3 connected in series with a battery of voltage V as shown in figure (a).
As soon as the battery is connected to the capacitors in series, the electrons of charge -Q are transferred from negative terminal to the right plate of C3which pushes the electrons of same amount -Q from left plate of C3 to the right plate of C2 due to electrostatic induction. Similarly, the left plate of C2 pushes the charges of Q to the right plate of which induces the positive charge +Q on the left plate of C1 At the same time, electrons of charge -Q are transferred from left plate of C1 to positive terminal of the battery.
(a)
Capacitors connected in series
(b)
Equivalent capacitors CS
By these processes, each capacitor stores the same amount of charge Q. The capacitances of the capacitors are in general different, so that the voltage across each capacitor is also different and are denoted as V1, V2 and V3 respectively.
The total voltage across each capacitor must be equal to the voltage of the battery.
V = V1 + V2 + V3 ….. (1)
Since Q = CV, we have V = `"Q"/"C"_1 + "Q"/"C"_2 + "Q"/"C"_3`
Q = `(1/"C"_1 + 1/"C"_2 + 1/"C"_3)` .....(2)
If three capacitors in series are considered to form an equivalent single capacitor Cs shown in figure (b), then we have V = `"Q"/"C"_"s"`
Substituting this expression into equation (2) we get
V = `"Q"/"C"_"s" = "Q"(1/"C"_1 + 1/"C"_2 + 1/"C"_3)`
`1/"C"_"s" = 1/"C"_1 + 1/"C"_2 + 1/"C"_3` ...(3)
Thus, the inverse of the equivalent capacitance Cs of three capacitors connected in series is equal to the sum of the inverses of each capacitance. This equivalent capacitance Cs is always less than the smallest individual capacitance in the series.
APPEARS IN
संबंधित प्रश्न
Define capacitor reactance. Write its S.I units.
Two identical parallel plate capacitors A and B are connected to a battery of V volts with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant K. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.
Two metal spheres of capacitance C1 and C2 carry some charges. They are put in contact and then separated. The final charges Q1 and Q2 on them will satisfy
Two conducting spheres of radii R1 and R2 are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series−parallel connections.
It is required to construct a 10 µF capacitor which can be connected across a 200 V battery. Capacitors of capacitance 10 µF are available but they can withstand only 50 V. Design a combination which can yield the desired result.
The figure show a network of five capacitors connected to a 10V battery. Calculate the charge acquired by the 5μF capacitor.
- Charge on each capacitor remains same and equals to the main charge supplied by the battery.
- Potential difference and energy distribute in the reverse ratio of capacitance.
- Effective capacitance is even les than the least of teh individual capacitances.
Current versus time and voltage versus time graphs of a circuit element are shown in figure.
 |
 |
The type of the circuit element is ______.
Obtain the equivalent capacitance of the network shown in the figure. For a 300 V supply, determine the charge on each capacitor.
