Advertisements
Advertisements
Question
Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.
Advertisements
Solution
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
RELATED QUESTIONS
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 identical capacitors C1, C2 and C3 of capacitance 6 μF each are connected to a 12 V battery as shown.
Find
(i) charge on each capacitor
(ii) equivalent capacitance of the network
(iii) energy stored in the network of capacitors
The equivalent capacitance of the combination shown in the figure is _________ .
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 equivalent capacitance of the infinite ladder shown in figure between the points A and B.
Each of the plates shown in figure has surface area `(96/∈_0) xx 10^-12` Fm on one side and the separation between the consecutive plates is 4⋅0 mm. The emf of the battery connected is 10 volts. Find the magnitude of the charge supplied by the battery to each of the plates connected to it.
A parallel-plate capacitor has plate area 100 cm2 and plate separation 1⋅0 cm. A glass plate (dielectric constant 6⋅0) of thickness 6⋅0 mm and an ebonite plate (dielectric constant 4⋅0) are inserted one over the other to fill the space between the plates of the capacitor. Find the new capacitance.
Find the capacitances of the capacitors shown in figure . The plate area is Aand the separation between the plates is d. Different dielectric slabs in a particular part of the figure are of the same thickness and the entire gap between the plates is filled with the dielectric slabs.
Calculate the resultant capacitances for each of the following combinations of capacitors.
A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system ______.
The positive terminal of 12 V battery is connected to the ground. Then the negative terminal will be at ______.
- 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.
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 ______.
A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage V. The battery is disconnected and an uncharged capacitor (B) of capacitance 2C is connected across A. Find the ratio of final charges on A and B.
Eight drops of mercury of equal radius and possessing equal charge combine to form a big drop. The capacitance of bigger drop as compared to each small drop is ______.
