Electrical CircuitsSeries Circuit and Parallel Circuit

Electrical Circuits

• Electric circuit consists of any number of elements joined at terminal points, providing at least one closed path through which charge can flow

• + terminal of battery attracts the electrons through the wire at the same rate at which electrons are supplied by the – terminal

• Two types: (1) Series circuit (2) Parallel circuit

Series Circuit and Parallel Circuit

Two elements are in series if one is connected end on end and have only one terminal in common and the common point is not connected to another current carrying element Characteristics of series circuit• current is same through all the resistors • voltage drop across each is different depending on its

resistance and • sum of the three voltage drops is equal to the voltage

applied across the resistors.

Series Circuit • Voltage drop across each resistor (using Ohm’s) is

V1 = I. R1, V2 = I. R2, V3 = I. R3

• Voltage applied = Sum of the voltage drops

E = V1 + V2 + V3 = I. R1 + I. R2 + I. R3

E = I (R1 + R2 + R3)

But E = I R, R = Equivalent resistance of the series combination

So I R = = I (R1 + R2 + R3)

• R = R1 + R2 + R3

Series Circuit

• Power delivered to each resistor

P1 = V1I = I2R1 = V12/R1, P2 = V2I = I2R2 = V2

2/R2,

and P3 = V3I = I2R3 = V32/R3

• The power delivered by the source, P = E I

• The total power delivered to a resistive network is equal to the total power dissipated by the resistive elements.

• That is, Pdel = P1 + P2 + P3 + ……

Series Circuit

• Ex: (a) Find the total resistance for the series circuit of Fig. 2.3. (b) Calculate the source current IS.

(c) Determine the voltages V1, V2 and V3 .(d) Calculate the power dissipated by R1, R2, and R3.(e) Determine the power delivered by the source, and compare it to the sum

of the powers dissipated in the resistor R1, R2, and R3.

Parallel Circuit

Two elements, branches, or networks are in parallel if they have two points in common as shown in Fig.

All the elements have terminals a and b in common

Characteristics of parallel circuit– potential difference across all resistance is the same,– current in each resistor is different and is given by

Ohm’s law and – total current is the sum of the three separate currents

Terminals of battery are connected directly across resistors R1 and R2(Fig.2.5)

I1 = E/R1, I2 = E/R2,

And I = I1 + I2 = E/R1 + E/R2 = E( 1/R1 + 1/R2)

And I = E/R, where R is equivalent resistance of the parallel combination

So, E/R = E( 1/R1 + 1/R2) so 1/R = 1/R1 + 1/R2

If n number of resistors are connected in parallel as in Fig.2.6

Total resistance

Parallel Circuits

Parallel Circuits Voltage across parallel elements is the same

A

Parallel Circuits

For the parallel network of Fig. 2.7, a) Calculate RT, (b) Determine IS, (c) Calculate I1 and I2 and demonstrate that IS = I1 + I2.(d) Determine the power to each resistor(e) Determine the power delivered by the source, and compare it to the total power dissipated by the resistors.

Parallel circuit

Kirchhoff’s voltage law

Kirchhoff’s voltage law (KVL) states that the algebraic sum of the potential rises and drops around a closed loop (or path) is zero. To apply Kirchhoff’s voltage law, the summation of potential rises and drops must by made in one direction around the closed loop. A plus sign is assigned to a potential rise – to +) and a minus sign to a potential drop (+ to -).

According to Kirchhoff’s voltage law from Fig.

Applied voltage = sum of voltage drops in series elements

that is, the applied voltage of a series circuit equals the sum of the voltage drops across the series elements. Kirchhoff’s can also be stated as

Ex: Determine the unknown voltages for Fig. 2.10.

Ex: For the circuit of Fig. 2.11:(a)Determine V2 using Kirchhoff’s Voltage law.(b)Determine I.(c) Find R1 and R2.

Kirchhoff’s voltage law

Voltage divider rule

•In series circuits, the voltage across the resistive elements will divide as the magnitude of the resistive levels

•Voltage divider rule (VDR) permits determining the voltage levels without first finding the current

•VDR can be derived by analyzing the network

• Applying Ohm’s law

•In general, VDR

• VDR states that the voltage across a resistor in a series circuit is equal to the value of that resistor times the total impressed voltage across the series elements divided by the total resistance of the series elements

Voltage divider rule

Example: Using voltage divider rule, determine V1 and V3 for the series circuit of Fig. 2.13.

• EX : Design the voltage divider of Fig. 5.30 such that VR1 4VR2

• Total resistance •

Kirchhoff’s current law

•Kirchhoff’s current law states that the algebraic sum of the currents entering and leaving an area, system, or junction is zero.

•In other words, the sum of the currents entering an area, system, or junction must equal the sum of the currents leaving the area, system, or junction. •In equation form:

.

Kirchhoff’s current law

•Ex: Determine I1, I2, I3 and I4 for the network of Fig. 2.17 .

At a At b

At c At d

.

Current divider rule (CDR)

Current divider rule determines the current entering a set of parallel branches will split between the elements.

•For two parallel elements of equal value, the current will divide equally.•For parallel elements with different values, the smaller the resistance, the greater the share of input current.•For parallel elements of different values, the current will split with a ratio equal to the inverse of their resistor values.

Input current

and

Current I1 Current I2

Current divider rule (CDR)The current through any parallel branch is equal to the product of the total resistance of the parallel branches and the input current divided by the resistance of the branch through which the current is to be determined.

For the particular case of two parallel resistors, as shown

and

Current divider rule (CDR)

Ex: Determine the current I2 for network of Fig. 2.20 using current divider rule

Ex: Determine the magnitudes of currents I1, I2 and I3 for network of Fig. 2.21

Using CDR

Applying KCL

Using CDR again

Total current entering the parallel branches must equal that leaving

Open circuit (OC) and short circuits (SC)Open Circuit

• simply two isolated terminals not connected by an element of any kind, as shown in Fig.

• OC current must be always be zero• Voltage across OC can be determined by the system it is connected to• OC can have a p.d (voltage) across its terminals, but the current is always

zero amperes

Short circuit• a very low resistance, direct connection between the terminals of a

network, as shown in Fig. • Current through the short circuit can be any value, as determined by the

system is connected to• Voltage across SC will always by zero volts (V = IR = I (0) = 0 V)• SC can carry a current of a level determined by the external circuit, but p.d

(voltage) across its terminals is always zero volts