# Energy In Electric Circuits

## Subject of electric circuits. Energy consumed in electric circuits. Energy consumed in circuits in series and parallel. The amount of energy consumed in any resistor. Questions and its solutions.

Concept Of Energy In Electric Circuits

If an amount current flows through any electric components, an amount energy loss occur in this component.

This energy loss is the energy dissipated to the environment in the form of heat.

The amount of the energy of dissipated is depends to the power in the electric components.

Mechanical work in physics was given in the following formula.

 P = Amount Of work done Time elapsed

The definition of electrical power is as following.

 P = Work done by electric Time elapsed

The energy that consumed from any resistor is depend to the power of this resistor. More power consumes more energy.

Power in electric circuits was given in the formulas following .

P = I2.R

 P = V2 R

P = V*I

Since the energy is power consumed per unit time is

W = P.t

W = I2*R*t

 W = V2*t R

W = V*I*t

The power was ratio to the time elapsed of the work done.

 P = W t

The work done is equal to the multiplication of time and power. This multiplication also gives the energy consumed.

W = P*t

The greater the power of a resistor the more it many do the work. Of course, the greater the power of a resistor the more it many consumes energy.

The unit of energy consumed in the electric circuits is joule like others energy units.

1 Joule = 1 Watt*1 second

1 Watt = (1 A)2 * 1 Ohm

1 J = 1.A2 *Ohm*second

Concept Of The Horsepower

Is called 1 horsepower to the power of 745.7 Watts. The horsepower is represented by hp.

The horsepower is taken 746 Watts approximately.

1 kW = 1000 Watt

1 kW = 1000/746

1 kW = 1,34 hp

Example: In the circuit shown in the figure, R1 = 6 Ω, R2 = 4 Ω, R3 = 2 Ω, R4 = 4 Ω, R5 = 20 Ω, R6 = 5 Ω, R7 = 4 Ω, R8 = 16 Ω

The voltage of the supply source is 110 V.

A) Find the power in each resistor.

B) Find the total power drawn from the source.

C) Find the energy consumed in 10 minutes in each resistor.

D) Find the total energy consumed in 10 minutes in the circuit.

Solution:

First we will find the equivalent resistance of the circuit. Then we will find main current of the circuit.

Then we will calculate current flowing through each resistor.

After finding the current flowing through each resistor, we can do calculations the power and energy.

The equivalent resistance of the resistors R1, R2 and R3 on upper arm.

R1-3 = 6 + 4 + 2

R1-3 = 12 Ω

The equivalent resistance of the lower arm resistors.

 R5,6 = 20*5 25

R5,6 = 4 Ω

R4-7 = 4 + 4 + 4

R4-7 = 12 Ω

The resistor R1-3 and the resistor R4-7 are parallel. The equivalent resistance of these resistors is

 R1-7 = 12 2

R1-7 = 6 Ω

The resistor R8 is connect to these resistors in series.

R1-8 = 6 +16

R1-8 = 22 Ω

The equivalent resistance of the circuit is

Rs = 22 Ω

The main current of the circuit is

 Is = 110 22

Is = 5 A

Suppose, the current flowing through the resistors R1, R2 and R3 is I1.

 I1 = R4-7 *Is R4-7 + R1-3

 I1 = 5*12 24

I1 = 2,5 A

Suppose, the current flowing through the arm which found the resistors R4-7  is I2.

I2 = 5 – 2,5 = 2,5 A

The current flows through resistors R1, R2 and R3 on upper arm is 2.5 A.

PR1 = (2.5)2*6

PR1 = 37.5 W

PR2 = (2.5)2*4

PR2 = 6.25*4

PR2 = 25 W

PR3 = (2.5)2*2

PR3 = 12.5 W

The current flows through resistors R4-7 in lower arm is 2.5 A.

PR4 = (2.5)2*4

PR4 = 25 W

The current flows through resistor R5 is

 IR5 = 2.5*5 25

IR5 = 0,5 A

The current flows through resistor R6 is

IR6 = 2,5 – 0,5 = 2 A

The power in the resistor R5 is

PR5 = (0.5)2*20

PR5 = 5

The power in the resistor R6 is

PR6 = 22*5

PR6 = 20 W

The current flows through the resistor R7 is 2.5 A.

PR7 = 6.25*4

PR7 = 25 W

The current flows through the resistor R8 is 5 A.

PR8 = 52 *16

PR8 = 400 W

B) The total power drawn from source is

Ptotal = 37.5 + 25 + 12.5 + 25 + 5 + 20 + 25 + 400

Ptotal = 550 W

Or

Ptotal = V*I

Ptotal = 110*5 = 550 W

C) The energy consumed in 10 minutes in each resistor

10 minutes = 10*60 = 600 seconds

WR1 = PR1*600

WR1 = 37,5*600

WR1 = 22500 J = 22,5 kJ

WR2 = 25*600 = 15000 J = 15 kJ

WR3 = 12,5*600 = 7500 J = 7,5 kJ

WR4 = 25*600 = 15000 J = 15 kJ

WR5 = 5*600 = 3000 J = 3 kJ

WR6 = 20*600 = 12000 J = 12 kJ

WR7 = 25*600 = 15000 J = 15 kJ

WR8 = 400*600 = 240000 J = 240 kJ

D) The total energy consumed in 10 minutes in the circuit.

Wtotal = 22.5 + 15 + 7.5 + 15 + 3 + 12 + 15 + 240

Wtotal = 330 kJ

Or

Wtotal = Ptotal*600

Wtotal = 550*600 = 330 000 J

Wtotal = 330 kJ

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December 1 2018

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