Advertisements
Advertisements
प्रश्न
Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.
Advertisements
उत्तर
Capacitance of capacitor C1 is 100 pF.
Capacitance of capacitor C2 is 200 pF.
Capacitance of capacitor C3 is 200 pF.
Capacitance of capacitor C4 is 100 pF.
Supply potential, V = 300 V
Capacitors C2 and C3 are connected in series.
Let their equivalent capacitance be C'
∴ `1/"C'" = 1/200 + 1/200 = 2/200`
∴ C' = 100 pF
Capacitors C1 and C' are in parallel. Let their equivalent capacitance be C''.
∴ `"C''" = "C'" + "C"_1`
= 100 + 100
= 200 pF
C'' and C4 are connected in series. Let their equivalent capacitance be C.
∴ `1/C = 1/("C''") + 1/("C"_4)`
= `1/200 + 1/100`
= `(2 + 1)/200`
C = `200/3` pF
Hence, the equivalent capacitance of the circuit is `200/3` pF.
Potential difference across C" = V"
Potential difference across C4 = V4
∴ `"V''" + "V"_4 = "V" = 300 "V"`
Charge on C4 is given by
Q4 = CV
= `200/3 xx 10^-12 xx 300`
= `2 xx 10^-8 "C"`
∴ `"V"_4 = "Q"_4/"C"_4`
= `(2 xx 10^-8)/(100 xx 10^-12)` = 200 V
∴ Voltage across C1 is given by
`"V"_1 = "V" - "V"_4`
= `300 - 200 = 100 "V"`
Hence, potential difference, V1, across C1 is 100 V.
Charge on C1 is given by,
`"Q"_1 = "C"_1"V"_1`
= `100 xx 10^-12 xx 100`
= `10^-8 "C"`
C2 and C3 have the same capacitances have a potential difference of 100 V together. Since C2 and C3 are in series, the potential difference across C2 and C3 is given by,
V2 = V3 = 50 V
Therefore, charge on C2 is given by,
`"Q"_2 = "C"_2"V"_2`
= `200 xx 10^-12 xx 50`
= `10^-8 "C"`
And charge on C3 is given by,
`"Q"_3 = "C"_3"V"_3`
= `200 xx 10^-12 xx 50`
= `10^-8 "C"`
Hence, the equivalent capacitance of the given circuit is `200/3` pF with
Q1 = 10−8 C, V1 = 100 V
Q2 = 10−8 C, V2 = 50 V
Q3 = 10−8 C, V3 = 50 V
Q4 = 2 × 10−8 C, V4 = 200 V
APPEARS IN
संबंधित प्रश्न
Define capacitor reactance. Write its S.I units.
A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.
A capacitor has capacitance C. Is this information sufficient to know what maximum charge the capacitor can contain? If yes, what is this charges? If no, what other information is needed?
Two capacitors each having capacitance C and breakdown voltage V are joined in series. The capacitance and the breakdown voltage of the combination will be
A parallel-plate capacitor has plate area 25⋅0 cm2 and a separation of 2⋅00 mm between the plates. The capacitor is connected to a battery of 12⋅0 V. (a) Find the charge on the capacitor. (b) The plate separation is decreased to 1⋅00 mm. Find the extra charge given by the battery to the positive plate.
Find the charges on the three capacitors connected to a battery as shown in figure.
Take `C_1 = 2.0 uF , C_2 = 4.0 uF , C_3 = 6.0 uF and V` = 12 volts.
Find the charge supplied by the battery in the arrangement shown in figure.
Each of the capacitors shown in figure has a capacitance of 2 µF. find the equivalent capacitance of the assembly between the points A and B. Suppose, a battery of emf 60 volts is connected between A and B. Find the potential difference appearing on the individual capacitors.
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.
Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.
Consider the situation shown in the figure. The switch S is open for a long time and then closed. (a) Find the charge flown through the battery when the switch S is closed. (b) Find the work done by the battery.(c) Find the change in energy stored in the capacitors.(d) Find the heat developed in the system.
An air-filled parallel-plate capacitor is to be constructed which can store 12 µC of charge when operated at 1200 V. What can be the minimum plate area of the capacitor? The dielectric strength of air is `3 xx 10^6 "Vm"^-1`
A parallel-plate capacitor with the plate area 100 cm2 and the separation between the plates 1⋅0 cm is connected across a battery of emf 24 volts. Find the force of attraction between the plates.
The variation of inductive reactance (XL) of an inductor with the frequency (f) of the ac source of 100 V and variable frequency is shown in fig.
- Calculate the self-inductance of the inductor.
- When this inductor is used in series with a capacitor of unknown value and a resistor of 10 Ω at 300 s–1, maximum power dissipation occurs in the circuit. Calculate the capacitance of the capacitor.
A capacitor of 4 µ F is connected as shown in the circuit (Figure). The internal resistance of the battery is 0.5 Ω. The amount of charge on the capacitor plates will be ______.
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 5µF capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5 µF capacitor If the energy change during the charge redistribution is `"X"/100`J then value of X to the 100 nearest integer is ______.
