Advertisements
Advertisements
Question
The two square faces of a rectangular dielectric slab (dielectric constant 4⋅0) of dimensions 20 cm × 20 cm × 1⋅0 mm are metal-coated. Find the capacitance between the coated surfaces.
Advertisements
Solution
The area of the plates of the capacitor is given by
`A = 20 "cm" xx 20 "cm" = 400 "cm"^2`
⇒ `A = 4 xx 10^-2 "m"`
The separation between the parallel plates is given by
`d = 1 "m" = 1 xx 10^-3 "m"`
Here, the thickness of the dielectric is the same as the separation between the parallel plates.
Thus, the capacitance is given by
`C = (∈_0Ak)/d = ((8.85 xx 10^-12) xx (4 xx 10^-2) xx 4)/10^-3 = 1.42 "nF"`
APPEARS IN
RELATED QUESTIONS
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
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
Each capacitor shown in figure has a capacitance of 5⋅0 µF. The emf of the battery is 50 V. How much charge will flow through AB if the switch S is closed?
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.
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.
A capacitor is formed by two square metal-plates of edge a, separated by a distance d. Dielectrics of dielectric constant K1 and K2 are filled in the gap as shown in figure . Find the capacitance.
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.
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.
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.
Obtain the expression for capacitance for a parallel plate capacitor.
Obtain the expression for energy stored in the parallel plate capacitor.
Derive the expression for resultant capacitance, when the capacitor is connected in series.
Calculate the resultant capacitances for each of the following combinations of capacitors.
For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor.
The thickness of the dielectric slab is `3/4`d, where 'd' is the separation between the plate of the parallel plate capacitor.
The new capacitance (C') in terms of the original capacitance (C0) is given by the following relation:
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 ______.
Two identical capacitors are connected as shown and have an initial charge of Q0. The separation between the plates of each capacitor is d0. Suddenly the left plate of the upper capacitor and right plate of the lower capacitor start moving with speed v towards the left while the other plate of each capacitor remains fixed. `("given" (Q_0V)/(2d_0) = 10 A)`. The value of current in the circuit is ______ A.
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?
