Unit 1

Basic Circuit Concept

1.1             Basic circuit elements R, L and C

Resistor

Control the flow of current

V=IR

P=I2R

Behaviour of Resistance-

t=0-  t=0   t=0+  t=∞

R    R      R     R

Inductor

1. Active - FET, diode
2. Passive - R, L, C

Storage of energy

Based on electromagnetic induction

Faraday’s Law

Φ∝ i

Φ = L.i

Relaxed inductor I0 = 0 

Current Carrying Inductor:  

L = L1+L2

Capacitor:

Charge storing device (voltage)

Q ∝ V

Q = C V

Relaxed capacitor

charged capacitor

Electrostatic Energy

Inductor do not respond any change as far as current is concerned.

Capacitor does not respond any change as far as voltage is concerned.

Definition of Open circuit and short circuit

R=∞

V=0  or V≠ 0

I=0

Short Circuit: 

V = 0

R = 0

I may or may not be zero

1.2             Classification of circuit elements

1)     Active and Passive Elements:

The elements which deliver power or energy are called as Active elements. For example: Transistor, Voltage and Current source.

The elements which absorb power are called as passive elements. For example: Resistor, Inductor and capacitor. 

2)     Unilateral and Bilateral Elements:

The unilateral elements allow the flow if current in only one direction. Ex. Diode.

The bilateral element allows the flow of current in both the directions. Ex. Resistor, inductor and capacitor.

3)     Linear and Non-Linear:

The elements which obey ohms law or have linear relationships are known as Linear elements. Ex. Resistor, inductor and capacitor.

The elements which do not obey ohms law are known as Non-Linear elements.

1.3             voltage and current sources

1. Voltage Source: A voltage source always have a resistance in series. 

Ideal source

R = 0

Practical = 2 - 5Ω

I = 0

2.     Current Source: Always have R parallel with the source.

Ideal and Practical Sources (Independent Sources only)

Ideal and practical Voltage and Current source:

A voltage source is a device which provides a constant voltage to load at any instance of time and is independent of the current drawn from it. This type of source is known as an ideal voltage source. Practically, the ideal voltage source cannot be made. It has zero internal resistance. It is denoted by this symbol.

Fig:  Voltage source symbol

Ideal Voltage Source

Fig: Ideal Voltage Source

The graph represents the change in voltage of the voltage source with respect to time. It is constant at any instance of time.

Voltage sources that have some amount of internal resistance are known as a practical voltage source. Due to this internal resistance, voltage drop takes place. If the internal resistance is high, less voltage will be provided to load and if the internal resistance is less, the voltage source will be closer to an ideal voltage source. A practical voltage source is thus denoted by a resistance in series which represents the internal resistance of source.

Practical Voltage source

Fig: Practical Voltage source

The graph represents the voltage of the voltage source with respect to time. It is not constant but it keeps on decreasing as the time passes.

Current source

A current source is a device which provides the constant current to load at any time and is independent of the voltage supplied to the circuit. This type of current is known as an ideal current source; practically ideal current source is also not available. It has infinite resistance. It is denoted by this symbol.

Ideal Current source

Fig: Ideal Current source

The graph represents the change in current of the current source with respect to time. It is constant at any instance of time.

Why ideal Current source has infinite resistance?

A current source is used to power a load, so that load will turn on. We try to supply 100% of the power to load. For that, we connect some resistance to transfer 100% of power to load because the current always takes the path of least resistance. So, in order for current to go to the path of least resistance, we must connect resistance higher than load. This is why we have the ideal current source to have infinite internal resistance. This infinite resistance will not affect voltage sources in the circuit.

Practical Current source

Practically current sources do not have infinite resistance across there but they have a finite internal resistance. So, the current delivered by the practical current source is not constant and it is also dependent somewhat on the voltage across it.

A practical current source is represented as an ideal current source connected with resistance in parallel.

Fig; Practical Current source

The graph represents the current of the current source with respect to time. It is not constant but it also keeps on decreasing as the time passes.

1.4 Kirchoff’s laws

Statement: the algebraic summation of all Voltage in any closed circuit or mesh of loop zero.

Ie ∑ Voltage in closed loop = 0 the summation of the Voltage rise (voltage sources) is equal to summation of the voltage drops around a closed loop in 0 circuit for explanation from here

Determination of sigh and direction of currents (Don’t write in exams just for understanding)

Current entering a resistor is +ve and leaving should be –ve

Now

Potential Rise    Potential Drop

We are reading from +V to –V  we are reading from –V to +V

potential drops     potential rise

-V       +V

Given Circuit

First identify no of loops and assign direction of current flowing in loop

Note: no of loops in circuit = No, of unknown currents = no, of equations in the circuit

Note: keep loop direction and current direction same i.e either clockwise or anticlockwise for all loops I1 I2

Now according to direction of direction assign signs (+ve to –ve) to the resistors

Note: voltage sources (V) polarities does not change is constant.

Note: for common resistor between 2 loops appearing in the circuit like R3 give signs according to separate loops as shown

    When considering only loop no 1 (+ R3 - )

-         B

Now consider diagram A and write equations

Two loops two unknown currents two equation

Apply KVL for loop ① [B. Diagram]

(+ to  drop-) = - sign and (- to rise +) = + sign

for drop = -sign

for rise = + sign

-

-() R2 is considered because in R3,2 currents are flowing and   and we have taken () because we are considering loop no 1 and current flowing is in loop no 1

)

Similarly, for loop no. 2 currents flowing is resistor R3 it should be )R3

Consider loop no. 1 apply KVL

- …….①

-

Consider loop no. 2 apply KVL

-…….②

-

After solving equation ① and ② we will get branch current and

1.5 Star-delta and Delta to Star transformations

Star-Delta

Delta-Star

RA=

RB=

RC=

1.6 Network reduction techniques, Simple problems

Q1) For the circuits given below write the voltage equations:

Solution: Let current i1be in loop 1 current and i2 for loop 2 

Q2) For the circuits given below write the voltage equations

Solution:

For loop 1 

For loop 2 

Q3) Using nodal analysis find voltage across 5resistor.

Solution:

For V1

      1

For V2

     2

Solving 1 and 2:

For 5 voltage =

= -50.9 + 57.27

= 6.37V

Q4)Find

Sol:

Q5) Find

Sol: 

Q6) . Find the current through resistance.

Solution:

1= 0

2=

1 + 2 

Special Case:

Since two voltage sources with different magnitude in parallel which cannot be connected as in single branch two different current is not possible (if 5V than I = zero).

Q7)

1 =

2 =

=

1 + 2

=

Q8) Use nodal analysis to find current in the circuit?

Sol: + +3i=4

+ -3i= -3

But i=

Substituting and solving above equation we get

V2 = 10V

i= = 2A

Q9) Find equivalent resistance R?

Sol: Equivalent resistance across ab = = 4Ω

Equivalent resistance across cd = =1 Ω

Req = Rab||Rcd +3 = + 3 = 19/5 Ω