Advertisements
Advertisements
प्रश्न
Find the equivalent capacitances of the combinations shown in figure between the indicated points.
Advertisements
उत्तर
Applying star-delta conversion in the part indicated in the diagram.
The Capacitance of the `C_1` is given by
`C_1^' = (C_2C_3)/(C_1+C_2+C_3)`
`C_2^' = (C_1C_3)/(C_1+C_2+C_3)`
`C_3^' = (C_1C_2)/(C_1+C_2+C_3)`
⇒ `C_1'^ = (3 xx 4)/(1+3+4) = 12/8 "uF"`
⇒ `C_2^' = (1 xx 3)/(1+3+4) = 3/8 "uF"`
⇒ `C_3^' = (1 xx 4)/(1+3+4) = 4/8 "uF"`
Thus, the equivalent circuit can be drawn as :
Therefore, the equivalent capacitance is given by
`C_(eq) = 3/8 + [((3+1/2) xx (3/2+1))/((3+1/2)+(3/2+1))]` = `3/8 + 35/24 = (9+35)/24 = 11/6 "uF"`
`1+1 = 2 "uF"`
(c)
It is a balanced bridge.
Therefore, the capacitor of capacitance 5 μF can be removed.
Cef = `4/3+8/3+4 = 8 "uF"`
The capacitance of the two branches are :
`C_1 = (2 xx 4)/(2+4) = 4/3 uF`
`C_2 = (4 xx 8)/(4+8) = 8/3 uF`
∴ Equivalent capacitance = `4/3 + 8/3 + 4 = 8 "uF"`
It can be observed that the bridges are balanced.
Therefore, the capacitors of capacitance 6 μF between the branches can be removed
The capacitances of the four branches are :
`C_1 = (2 xx 4)/(2+4) = 4/3 uF`
`C_2 = (4 xx 8)/(4+8) = 8/3 uF`
`C_3 = (4 xx 8)/(4+8) = 8/3 uF`
`C_4 = (2 xx 4)/(2+4) = 4/3 uF`
∴ Equivalent capacitance
= `4/3 + 8/3 + 8/3 + 4/3`
= ` 8 "uF"`
APPEARS IN
संबंधित प्रश्न
When an AC source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero
A capacitor of capacitance C is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?
(i) charge stored by the capacitor.
(ii) Field strength between the plates.
(iii) Energy stored by the capacitor.
Justify your answer in each case.
A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5 µC. The space between the concentric spheres is filled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.
Three capacitors of capacitances 6 µF each are available. The minimum and maximum capacitances, which may be obtained are
Following operations can be performed on a capacitor:
X − connect the capacitor to a battery of emf ε.
Y − disconnect the battery.
Z − reconnect the battery with polarity reversed.
W − insert a dielectric slab in the capacitor.
(a) In XYZ (perform X, then Y, then Z) the stored electric energy remains unchanged and no thermal energy is developed.
(b) The charge appearing on the capacitor is greater after the action XWY than after the action XYZ.
(c) The electric energy stored in the capacitor is greater after the action WXY than after the action XYW.
(d) The electric field in the capacitor after the action XW is the same as that after WX.
Find the equivalent capacitance of the system shown in figure between the points a and b.
A parallel plate capacitor stores a charge Q at a voltage V. Suppose the area of the parallel plate capacitor and the distance between the plates are each doubled then which is the quantity that will change?
Obtain the expression for energy stored in the parallel plate 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.
When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance ______.
Three capacitors 2µF, 3µF, and 6µF are joined in series with each other. The equivalent capacitance is ____________.
Five capacitor each of capacitance value C are connected as shown in the figure. The ratio of capacitance between P to R, and the capacitance between P and Q is ______.
Between the plates of parallel plate condenser there is 1 mm thick medium shoot of dielectric constant 4. It is charged at 100 volt. The electric field in volt/meter between the plates of capacitor is ______.
The displacement current of 4.425 µA is developed in the space between the plates of the parallel plate capacitor when voltage is changing at a rate of 106 Vs-1. The area of each plate of the capacitor is 40 cm2. The distance between each plate of the capacitor is x × 10-3 m. The value of x is ______.
(Permittivity of free space, ε0 = 8.85 × 10-12C2N-1m-2).
A capacitor of capacity 2 µF is charged to a potential difference of 12 V. It is then connected across an inductor of inductance 0.6 mH. The current in the circuit at a time when the potential difference across the capacitor is 6.0 V is ______ × 10-1A.
A capacitor has charge 50 µC. When the gap between the plate is filled with glass wool, then 120 µC charge flows through the battery to capacitor. The dielectric constant of glass wool is ______.
Current versus time and voltage versus time graphs of a circuit element are shown in figure.
 |
 |
The type of the circuit element is ______.
A capacitor with capacitance 5µF is charged to 5 µC. If the plates are pulled apart to reduce the capacitance to 2 µF, how much work is done?
