Capacitors:

Capacitor is a two terminal electronic component used to store charge consists of two conducting plates and separated by dielectric.

the ability of capacitor to store charge is called capacitance and it measured in coulomb’s per volt or farads. The unit farad named after Michael Faraday. Capacitors can be fixed and variable. When we apply charge to one terminal of capacitor then one side got +ve charge and other side got -ve charge and charge on the plates are directly proportional to applied voltage.

q = Cv   -(A)

where C is proportionality constant.

How Capacitors works?

When we apply the potential across the terminals then charge differential between the plates creates electric field that stores energy. Negative particles start moving towards +ve terminal of battery and then

towards the other plate with the passage of time one plate +ve and other is -ve charge at this stage capacitor is fully charged but our area of interest is current-voltage characteristics of capacitor, so current is

i = dq / dt  -(1)

In equation we take the derivative of charge with respect to time

rearranging the eq.                                                             i = q d / dt  -(2)

Inserting values of ->A in eq.2

i = C dv / dt

Work done for capacitors calculated by using formula

w = 1/2 . C v^2  (J)

w = q^2 / 2.C

both above equations represent the energy stored by capacitor, remember this is equal to the work done by the source to charge the capacitor.

Story “We know in capacitors when we apply potential current is directly proportional to voltage across capacitor but in case of dc voltage source we know that dc voltage does not vary with time so the current become zero. We treat capacitor as open circuit in case of dc source. In case of ideal capacitor when capacitor is fully charged charge remain in capacitor for a long time but when a connect a bulb with a capacitor then charge starts transferring to bulb a time reach when capacitor discharge then same process repeats”

Example:A 10F capacitor has an accumulated charge of 500C . Determine the voltage across capacitor

We know that        q = Cv

v = q / C  = 500 / 10 = 50V

Inductors:

Is a current conducting electronic wire usually in form of coil. How it looks and it’s symbol is

Basically inductors are categorized by type of core on which they wound. We can calculate the voltage across conductor by

v = L di / dt

while L proportionality constant called inductance measured in units henry. Power across the inductor is calculated in terms of current which is

w = 1/2 L i^2 (J)

same as in case of capacitor when we applied the potential voltage is directly proportional to the flowing current but in dc voltage does not vary with time so we also consider inductor as a open circuit so a circuit take form

before applying potential and after applying potential the circuit looks like.

Capacitor and Inductor Combinations:

Capacitor in Series:

We can find equivalent circuit by applying KVL to calculate capacitor in series same as resistors in parallel means take the reciprocal of capacitor and then add them

so there equivalent equation take form

                            1 / Ceq = 1 / C1 + 1 / C2 + 1 / C3 + . . . . .+ 1 / Cn

 Capacitor in Parallel:

                                    To determine capacitor in parallel we apply KCL so the capacitor in parallel is same as resistor in series.

 

it’s equivalent parallel equation is

Ceq = C1 + C2 + C3+ . . . . . . . + Cn

Series Inductors:

To determine the equivalent equation of inductors connected in series we can calculate there equivalent by applying KVL

                                                    Leq = L1 + L2 + L3 + . . . . . + Ln

Parallel Inductors:

To determine the equivalent equation of parallel inductors we apply KCL it’s equation is

 

1 / Leq = 1 / L1 + 1 / L2 + 1 / L3 + . . . . . + 1 / Ln

 

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