Advertisements
Advertisements
प्रश्न
Find the charges on the four capacitors of capacitances 1 μF, 2 μF, 3 μF and 4 μF shown in the figure.
Advertisements
उत्तर
When the capacitors are fully charged, they attain steady state and no current flows through them. Then, equivalent resistance of the circuit,
\[R_{eff} = \frac{3 \times 6}{3 + 6} = 2 \Omega\]
Current through the circuit,
\[i = \frac{6}{2} = 3 A\]
Current i is divided in the inverse ratio of the resistance in each branch. One branch has resistance of 3 Ω and the other branch has resistance of 6 Ω.
Current i' through the 3 Ω branch,
\[i' = \frac{6}{9}i = \frac{2}{3} \times 3 A = 2 A\]
Current i'' through the 6 Ω branch,
\[i'' = i - i' = 1 A\]
Voltage across the 1 Ω resistor = 2 A × 1 Ω = 2 V
Charge on the 1 μF capacitor = 2 × 1 μF = 2 μC
Voltage across the 2 Ω resistor = 2 Ω × 2 A = 4 V
Charge on the 2 μF capacitor = 4V × 2 μF = 8 μC
Voltage across each 3 Ω resistor = 3 Ω × 1 A = 3 V
Charge on the 4 μF capacitor = 3 × 4 μC = 12 μC
Charge on the 3 μF capacitor = 3 × 3 μC = 9 μC
APPEARS IN
संबंधित प्रश्न
Two capacitors of unknown capacitances C1 and C2 are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of C1 and C2. Also calculate the charge on each capacitor in parallel combination.
The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed loop a b c d a.
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.
An electrical technician requires a capacitance of 2 µF in a circuit across a potential difference of 1 kV. A large number of 1 µF capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors.
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 25 cm2 and separation 1⋅00 mm is connected to a battery of 6⋅0 V. Calculate the charge flown through the battery. How much work has been done by the battery during the process?
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
A wire of resistance ‘R’ is cut into ‘n’ equal parts. These parts are then connected in parallel with each other. The equivalent resistance of the combination is:
The figure shows a network of five capacitors connected to a 100 V supply. Calculate the total energy stored in the network.
Two parallel plate capacitors X and Y, have the same area of plates and same separation between plates. X has air and Y with dielectric of constant 2, between its plates. They are connected in series to a battery of 12 V. The ratio of electrostatic energy stored in X and Y is ______.
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:
Two equal capacitors are first connected in series and then in parallel The ratio of the equivalent capacities in the two cases will be ______.
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. What is the total capacitance of the combination?
