Advertisements
Advertisements
Question
Suppose a charge +Q1 is given to the positive plate and a charge −Q2 to the negative plate of a capacitor. What is the "charge on the capacitor"?
Advertisements
Solution
Given :
Charge on the positive plane = `+Q_1`
Charge on the negative plate = `-Q_2`
To calculate: Charge on the capacitor
Let ABCD be the Gaussian surface such that faces AD and BC lie inside plates X and Y, respectively.
Let q be the charge appearing on surface II. Then, the distribution of the charges on faces I, III and IV will be in accordance with the figure.
Let the area of the plates be A and the permittivity of the free space be `∈_0`.
Now, to determine q in terms of Q1 and Q2, we need to apply Gauss's law to calculate the electric field due to all four faces of the capacitor at point P. Also, we know that the electric field inside a capacitor is zero.
Electric field due to face I at point P, E1 = `(Q_1 - q)/(2∈_0A)`
Electric field due to face II at point P, E2= `(+q)/(2∈_0A)`
Electric field due to face III at point P, E3 = `(-q)/{2∈_0A)`
Electric field due to face IV at point P, E4 = `-((-Q_2+q)/(2∈_0A))` (Negative sign is used as point P lies on the LHS of face IV.)
Since point P lies inside the conductor,
E1 + E2 + E3 + E4 = 0
`therefore` `Q_1-q+q-q-(-Q_2+q)` = 0
⇒ q = `(Q_1+Q_2)/2`
Thus , the change on the capacitor is `(Q_1+Q_2)/2`, which is the charge on faces II and III.
APPEARS IN
RELATED QUESTIONS
A capacitor 'C', a variable resistor 'R' and a bulb 'B' are connected in series to the ac mains in circuit as shown. The bulb glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between the plates of the capacitor, keeping resistance R to be the same; (ii) the resistance R is increased keeping the same capacitance?
Three capacitors each of capacitance 9 pF are connected in series.
- What is the total capacitance of the combination?
- What is the potential difference across each capacitor if the combination is connected to a 120 V supply?
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. Determine the charge on each capacitor if the combination is connected to a 100 V supply.
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.
A circuit is set up by connecting inductance L = 100 mH, resistor R = 100 Ω and a capacitor of reactance 200 Ω in series. An alternating emf of \[150\sqrt{2}\] V, 500/π Hz is applies across this series combination. Calculate the power dissipated in the resistor.
The plates of a parallel-plate capacitor are given equal positive charges. What will be the potential difference between the plates? What will be the charges on the facing surfaces and on the outer surfaces?
The following figure shows two capacitors connected in series and joined to a battery. The graph shows the variation in potential as one moves from left to right on the branch containing the capacitors.
The separation between the plates of a charged parallel-plate capacitor is increased. Which of the following quantities will change?
(a) Charge on the capacitor
(b) Potential difference across the capacitor
(c) Energy of the capacitor
(d) Energy density between the plates
A parallel-plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. The sheet remains parallel to the plates of the capacitor.
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.
A capacitor of capacitance 5⋅00 µF is charged to 24⋅0 V and another capacitor of capacitance 6⋅0 µF is charged to 12⋅0 V. (a) Find the energy stored in each capacitor. (b) The positive plate of the first capacitor is now connected to the negative plate of the second and vice versa. Find the new charges on the capacitors. (c) Find the loss of electrostatic energy during the process. (d) Where does this energy go?
Three capacitors of capacitance `C_1 = 3muf` , `C_2 = 6muf` , `C_3 = 10muf` , are connected to a 10V battery as shown in figure 3 below :
Calculate :
(a) Equivalent capacitance.
(b) Electrostatic potential energy stored in the system
The figure shows a network of five capacitors connected to a 100 V supply. Calculate the total energy stored in the network.
Three capacitors each of 4 µF are to be connected in such a way that the effective capacitance is 6µF. This can be done by connecting them:
In the following circuit, the equivalent capacitance between terminal A and terminal B is:
The equivalent capacitance of the combination shown is:
The potential difference that must be applied across the series and parallel combination of 4 identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is ______.
