Advertisements
Advertisements
प्रश्न
Deduce an expression for equivalent capacitance C when three capacitors C1, C2 and C3 connected in parallel.
Advertisements
उत्तर
An expression for effective capacitance in the parallel grouping of capacitors :
Consider three capacitors of capacitance C1 , C2 and C3 are connected in parallel.
Let Q1, Q2 and Q3 be the charges deposited on the capacitors as shown in the figure.
Suppose a potential difference ‘V ’ is applied across the combination. Then, the potential difference between the plates of each capacitor is V but charges on each capacitor are different. Since different current flows through different branches, so the charges are given by
`Q_1 = C_1V.Q_2 = C_2V. Q_3 = C_3V` ....(i)
From the principle of conservation of charge
`Q = Q_1 + Q_2 + Q_3`
`Q = C_1V + C_2V + C_3V` [From equation (i)]
`∴ Q = V(C_1 + C_2 + C_3)`
If these capacitors are replaced by a single capacitor of capacity CP such that `Q = C_PV` then using equation (ii) we have,
`C_PV = V(C_1+C_2+C_3)`
`C_P = C_1+C_2+C_3`
APPEARS IN
संबंधित प्रश्न
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.
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.
If the capacitors in the previous question are joined in parallel, the capacitance and the breakdown voltage of the combination will be
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
An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by `pi /4` . If element X is a pure resistor of 100Ω ,
(a) name the circuit element Y.
(b) calculate the rms value of current, if rms value of voltage is 141V.
(c) what will happen if the ac source is replaced by a dc source ?
An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by `pi/4`. If element X is a pure resistor of 100 Ω,
(a) name the circuit element Y.
(b) calculate the rms value of current, if rms of voltage is 141 V.
(c) what will happen if the ac source is replaced by a dc source
The capacitors, each of 4 µF are to be connected in such a way that the effective capacitance of the combination is 6 µF. This can be achieved by connecting ______.
In the following circuit, the equivalent capacitance between terminal A and terminal B is:
