Parallel RL circuits formula and Phasor diagram explanation

Parallel  RL circuit formula and diagram

The current through L will lag  IR  by 90 degrees . The resultant negative phase angle  depends upon the relative values of R and XL. for R, E and R in phase . For  XL , E and IL in quadratic lagging current.

As  the circuit is inductive the phase angle is  negative.

Parallel RL circuit Phasor Diagram

There cannot be a direct addition of IR and IL because of their 90 degree phase angle. 

Parallel RL circuits formula

Series RLC circuit formula explanation

Series RLC circuit diagram and formula

Resistance ,inductance capacitance in series

  

In RLC series circuit , the series current is common for Resistance, Capacitance and inductance . VR will be in phase width I. Whereas the voltage of Vc and VL will be 180 degree phase opposition, resulting in some cancellation.

Series RLC  Phasor Diagram

The phasor diagram will produce the resultant circuit voltage and its phase angle. Positive angle indicate a greater inductive circuit influence and negative angle capacitive.

This is the corresponding formula for RLC circuit

Series RLC Formulas

The formula for Series RC circuit with Phasor Diagram

Series RC circuit formula explanation

 R- the resistance -opposition to current flow (ohms)Ω

C- capacitance-opposition to any change in voltage ,farad(f)

 VR=IR- voltage drop of the resistor

Vc= q/c=∫idt/c- voltage drop in the capacitor

     

     When a capacitor and a resistor  are in series current will flow to charge the capacitor .

 The two voltages VR and VC cannot be added directly and the phasor diagram is used  to find the resultant or the applied voltage amplitude and phase angle . 

Voltage VC can be found using Ohms law where VC = XC x I

The resultant or applied voltage is that which or developed across the circuit with these particular component values.  The resultant voltage can be greater than the individual values of VR and Vc   

As this is capacitive circuit the resultant voltage angle will lag the current I

Current I is shown as being in phase with VR . VC will lag I by 90.

Series RC circuit Phasor Diagram

Series RC circuit Formula

Here are the Formulas and the proof solution for the formula in RC circuit:

Series RC circuit Waveform

This is an example of a waveform produced by the   resultant voltage and corresponding resultant phase  angle.

Analyze the formula for Series RL circuit and its Phasor Diagram

   Series RL circuit

R- the resistance -opposition to current flow (ohms)Ω

L- Inductance -opposition to any change  

XL- inductive resistance

VR=I R volts

VL=I XL volts

XL = inductance reactance  (ohms) Ω

      = 2πfL= ωL

Voltage developed across R and L cannot be added directly. The phasor diagram is used to show the resultant voltage and phase angle.The resultant or the applied voltage will lead the current I which is given an arbitrary value in the instance to show that is in phase with VR

Phasor diagram Series RL circuit:

Series RL circuit Formula :

Series RL Circuit generated Waveform:

The larger the relative value of the  XL to R the closer the resultant phase angle willl be 90 degrees which is an indication of the amount of inductance in the circuit.

What are the effects of Electricity

The Effects of electricity
Electricity is  form of energy which could not be seen,but its presence could be detected due to numerous effects it has in  our daily living.

1. Mechanical effect  
An electric fan  for ventilation through the rotation of its blades; A vacuum cleaner that cleans our floors with dirt's.These devices operate because of electricity. Mechanical effect of electricity is made possible by the use of the device called the motor. The electricity powers up the motor in order for it to make work for the benefit of man.


2. Chemical Effect
The  best example for a chemical effect of electricity is Electroplating. It  involves the deposition of a thin protective layer  onto a prepared metal surface, using electrochemical processes.Applications of electroplating can be observed from the household equipments ,kitchen utensils,instruments common steel bolts ,nuts and washers and and even a fashion wear such as bracelets, earrings and necklaces which could either be Gold plated, silver plated, . Aluminum parts and steel parts in lighting fixtures are also electroplated.


3.Thermal Effect
  "A current of electricity passes over a conductor raises its temperature". That is why  heating elements requires an alloy of  metal to withstand  intense heat without melting. This heating elements are installed in our electric cooker, iron and heater.

4.Magnetic effects
Speakers produces varying sounds  because of magnetic effect. these devices have electromagnets  and a permanent magnet .. These two magnets  interact with each other. When the electrical current flowing through the voice coil changes direction, the coil's polar orientation reverses. This changes the magnetic forces between the electromagnet and the permanent magnet, moving the electromagnet and attached diaphragm back and forth . It pushes and pulls on the speaker cone  producing a vibration of the air in front of the speaker creating sound waves. 
5. Physiological Effect
Are you familiar with a treatment  known as "Shock Treatment or Shock Therapy" . This medical treatment is being utilized in rehabilitation centers to treat neurotic disorders


6.Photoelectric effect
  Wondering how did the doors in malls hotels and other buildings and offices opens automatically as soon as  you step the porch of these buildings? It is possible through photoelectric effect. These doors have "photo cells" This photocells have electrodes that are light sensitive that is used to operate a relay, which might turn a motor on to open a door or ring a bell in an alarm system. Same principle are also true in counting vehicles passing a road.

7.Luminous Effect
 " Light" this is the very common effect of electricity.  If however after you had switched on the means of control and the room is still not illuminated,then you'll surely say, there's an absence of electricity. To layman's language it is called a black out or brown out. But what is being implied here actually is that there's no electrical current in the circuit.