CBSE Class 12-science Answered
How can we identify NODES in a mixed or complex arrangement of CAPACITORS ? how to find CHARGE , POTENTIAL , CAPACITANCE on each capacitor ? Please give the explanation with the help of atleast 5 examples .
Asked by pardeepkumar2281 | 13 May, 2018, 08:22: AM
Expert Answer
Nodes are junction points in the circuit and we can identify the junction points with the following shapes
Nodal analysis of capacitive circuits based on conservation of charge.
At any isolated part of a circuit, charge is conserved. ∑qi = 0 if the capacitors are initially uncharged.
Isolated system and nodes are agin illustrated in the following figure.
Following steps should be followed in problem solving.
(1) Assume a node in the circuit as a reference and assume its potential is zero.
(2) Mark different nodes in the circuit and assign their potentials.
(3) Identify the isolated systems in the circuit and write the equation of conservation of charges.
(4) Solve the equations to get the values of potentials.
Let us learn this technique through some examples.
In the fig.A given below what are the charges on all capacitors ?
Let us assign the potential at nodes Nx and Ny as x and y respectively. Two isolated systems were identified and shown in fig.B. The potentials at diffrenet junctions are marked according to the EMF of batteries and the chosen reference point. The charge appearing on each capacitors are marked as per the formula q = CΔV.
In isolated system net charge should be conserved.
For the isolated system-1, we have 2(x-10)+4(x-y)+2x= 0 or 2x-y = 5 ..................(1)
For the isolated system-2, we have -4(x-y)+4(y-15)+2(y-5)= 0 or -2x+5y = 35 ..................(2)
solving (1) and (2) we get x = 7.5 V and y = 10 V.
Fig.B shows the charge on capacitors in terms of x and y. hence charge on each capacitor can be calculated using the values of x and y.
Answered by Thiyagarajan K | 18 May, 2018, 02:10: PM
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