Chapter 6 Electrostatic Potential and Capacitance (Electrostatics Part 6) – Physics free study material by TEACHING CARE online tuition and coaching classes

 Circuit With Resistors and Capacitors.

• A resistor may be connected either in series or in parallel with the capacitor as shown below

(2) Three states of RC circuits

• Initial state : e., just after closing the switch or just after opening the switch.
• Transient state : or instantaneous state e., any time after closing or opening the switch.
• Steady state : e., a long time after closing or opening the switch. In the steady state condition, the capacitor is charged or discharged.

• Charging and discharging of capacitor in series RC circuit : As shown in the following figure (i) when switch S is closed, capacitor start charging. In this transient state potential difference appears across capacitor as well as resistor. When capacitor gets fully charged the entire potential difference appeared across the capacitor and nothing is left for the [shown in figure (ii)]

æ         –t ö

• Charging : In transient state of charging charge on the capacitor at any instant Q = Q0ç1 – e RC ÷

and

ç            ÷

è            ø

æ         –t ö

potential difference across the capacitor at any instant

V = V0 ç1 – e RC ÷

ç            ÷

è            ø

• Discharging : After the completion of charging, if battery is removed capacitor starts In

transient state charge on the capacitor at any instant Q = Q0 e ^{–t / RC}

and potential difference cross the capacitor at

any instant

V = V0 e –t / CR .

• Time constant (t) : The quantity RC is called the time constant e., t = RC .

In charging : It is defined as the time during which charge on the capacitor rises to 0.63 times (63%) the

maximum value. That is when t = t = RC , Q = Q₀ (1 – e ^-1 ) = 0.639 Q₀          or

In discharging : It is defined as the time during which charge on a capacitor falls to 0.37 times (37%) of the initial charge on the capacitor that is when t = t = RC , Q = Q₀ (e ^-1 ) = 0.37Q₀

• Mixed RC circuit : In a mixed RC circuit as shown below, when switch S is closed current flows through the branch containing resistor as well as through the branch contains capacitor and resistor (because capacitor is in the process of charging)

When capacitor gets fully charged (steady state), no current flows through the line in which capacitor is

connected. Therefore the current through resistor

V

R1 is (R + r

) , hence potential difference across resistance will be

equal to (

V0

R1 + r

1

) R₁ . The same potential difference will appear across the capacitor, hence charge on capacitor in

steady state

Q = CV0 R1

(R1  + r )

Network Solving.

To solve capacitive network for equivalent capacitance following guidelines should be followed. Guideline 1.     Identify the two points across which the equivalent capacitance is to be calculated. Guideline 2.     Connect (Imagine) a battery between these points.

Guideline 3.     Solve the network from the point (reference point) which is farthest from the points between which we have to calculate the equivalent capacitance. (The point is likely to be not a node)

• Simple circuits : Suppose equivalent capacitance is to be determined in the following networks between points A and B

• Circuits with extra wire : If there is no capacitor in any branch of a network then every point of this branch will be at same Suppose equivalent capacitance is to be determine in following cases

• Wheatstone bride based circuit : If in a network five capacitors are arranged as shown in following

figure, the network is called wheatstone bridge type circuit. If it is balanced then and equivalent capacitance between A and B

C1 = C3 C2           C4

hence C₅

is removed

• Extended wheatstone bridge : The given figure consists of two wheatstone bridge connected One bridge is connected between points AEGHFA and the other is connected between points EGBHFE.

This problem is known as extended wheatstone bridge problem, it has two branches EF and GH to the left and right of which symmetry in the ratio of capacities can be seen.

It can be seen that ratio of capacitances in branches AE and EG is same as that between the capacitances of the branches AF and FH. Thus, in the bridge AEGHFA; the branch EF can be removed. Similarly in the bridge EGBHFE branch GH can be removed

• Infinite chain of capacitors : In the following figure equivalent capacitance between A and B

(6)

Network with more than one cell :

• Advance case of compound dielectrics : If several dielectric medium filled between the plates of a parallel plate capacitor in different ways as