Advertisements
Advertisements
Question
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.
Advertisements
Solution
The given system of the capacitor will behave as two capacitors connected in series.
Let the capacitances be C1 and C2.
Now,
`C_1 = (∈_0Ak_1)/d_1` and `C_2 = (∈_0Ak_2)/d_2`
Thus, the net capacitance is given by
`C = (C_1C_2)/(C_1+C_2)`
= `((∈_0Ak_1)/d_1 xx (∈_0Ak_2)/d_2)/((∈_0Ak_1)/d_1 +(∈_0Ak_2)/d_2)`
= `(∈_0A(k_1+k_2))/(k_1d_2+k_2d_1)`
= `((8.85 xx 10^-12) xx (10^-2) xx 24) / ((6 xx 4 xx 10^-3 + 4 xx 6 xx 10^-3)) = 4.425 xx 10^-11 C`
= 44.25 pF
APPEARS IN
RELATED QUESTIONS
(i) Find equivalent capacitance between A and B in the combination given below. Each capacitor is of 2 µF capacitance.
(ii) If a dc source of 7 V is connected across AB, how much charge is drawn from the source and what is the energy stored in the network?
A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360 μC. When potential across the capacitor is reduced by 120 V, the charge stored in it becomes 120 μC.
Calculate:
(i) The potential V and the unknown capacitance C.
(ii) What will be the charge stored in the capacitor, if the voltage applied had increased by 120 V?
A thin metal plate P is inserted between the plates of a parallel-plate capacitor of capacitance C in such a way that its edges touch the two plates . The capacitance now becomes _________ .
Three capacitors of capacitances 6 µF each are available. The minimum and maximum capacitances, which may be obtained are
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.
A capacitor of capacitance 10 μF is connected to a battery of emf 2 V. It is found that it takes 50 ms for the charge of the capacitor to become 12.6 μC. Find the resistance of the circuit.
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.
Suppose the space between the two inner shells is filled with a dielectric of dielectric constant K. Find the capacitance of the system between A and B.
The figure show a network of five capacitors connected to a 10V battery. Calculate the charge acquired by the 5μF capacitor.
Three capacitors C1 = 3μF, C2 = 6μF, and C3 = 10μF are connected to a 50 V battery as shown in Figure below:
Calculate:
(i) The equivalent capacitance of the circuit between points A and B.
(ii) The charge on C1.
Three circuits, each consisting of a switch 'S' and two capacitors, are initially charged, as shown in the figure. After the switch has been closed, in which circuit will the charge on the left-hand capacitor
(i) increase,
(ii) decrease, and
(iii) remains the same? Give reasons.
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 capacitance for a parallel plate capacitor.
Derive the expression for resultant capacitance, when the capacitor is connected in parallel.
Calculate the resultant capacitances for each of the following combinations of capacitors.
The capacitance of a parallel plate capacitor is 60 µF. If the distance between the plates is tripled and area doubled then new capacitance will be ______.
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 ______.
Two plates A and B of a parallel plate capacitor are arranged in such a way, that the area of each plate is S = 5 × 10-3 m 2 and distance between them is d = 8.85 mm. Plate A has a positive charge q1 = 10-10 C and Plate B has charge q2 = + 2 × 10-10 C. Then the charge induced on the plate B due to the plate A be - (....... × 10-11 )C
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.
