Advertisements
Advertisements
Question
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.
Advertisements
Solution
The capacitances of three capacitors are C1= 2 μF, C2= 4 μF and C3= 6 μF and the voltage of the battery (V) is 12 V.
As the capacitors are connected in parallel, the equivalent capacitance is given by
Ceq = C1 + C2 + C3
= `(2+4+6) uF = 12 uF = 12 xx 10^-6 "F"`
Due to parallel connection, the potential difference across each capacitor is the same and is equal to 12 V.
Therefore, the charge on each capacitor can be calculated as follows :
The charge on the capacitor of capacitance C1= 2 μF is given by
`Q_1 = C_1V = (2 xx 10^-6) xx 12 "C" = 24 xx 10^-6 "C" = 24 "uC"`
Similarly, the charges on the other two capacitors are given by
`Q_2 = C_2V = (4 xx 10^-6) xx 12 "C" = 48 xx 10^-6 "C" = 48 "uC"`
and
`Q_3 = C_3V = (6 xx 10^-6) xx 12 "C" = 72 xx 10^-6 "C" = 72 "uC"`
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 capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected? (b) The energy stored in the capacitor Justify your answer by writing the necessary expressions
A capacitor of capacitance ‘C’ is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor.
The capacitance of a capacitor does not depend on
When 1⋅0 × 1012 electrons are transferred from one conductor to another, a potential difference of 10 V appears between the conductors. Calculate the capacitance of the two-conductor system.
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.
The separation between the plates of a parallel-plate capacitor is 0⋅500 cm and its plate area is 100 cm2. A 0⋅400 cm thick metal plate is inserted into the gap with its faces parallel to the plates. Show that the capacitance of the assembly is independent of the position of the metal plate within the gap and find its value.
A parallel-plate capacitor of capacitance 5 µF is connected to a battery of emf 6 V. The separation between the plates is 2 mm. (a) Find the charge on the positive plate. (b) Find the electric field between the plates. (c) A dielectric slab of thickness 1 mm and dielectric constant 5 is inserted into the gap to occupy the lower half of it. Find the capacitance of the new combination. (d) How much charge has flown through the battery after the slab is inserted?
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`
The figure show a network of five capacitors connected to a 10V battery. Calculate the charge acquired by the 5μF capacitor.
Three capacitors are connected in a triangle as shown in the figure. The equivalent capacitance between points A and C is ______.
Define ‘capacitance’. Give its unit.
Obtain the expression for energy stored in the parallel plate capacitor.
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.
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 ______.
Consider two conducting spheres of radii R1 and R2 with R1 > R2. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.
Obtain the equivalent capacitance of the network shown in the figure. For a 300 V supply, determine the charge on each capacitor.
The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K1 and K2 with thickness `3/8 d and d/2`, respectively, are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If K1 = 1.25 K, the value of K1 is:
