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.

Using multimeter VOM as voltmeter for ACV test

The Ac voltmeter is used to measure alternative current voltage or electrical pressure of a circuit. This instrument is connected across the circuit and it does not require correct application of the polarity . The unit of measure is volt(V).

Note;

•  If the voltage range is unknown get the estimate value by setting the knob at the top level or should be   at 1000 V before measuring AC voltage,then adjust or lower the range until you could read it conveniently.
•   Do not touch the test probe.

Procedure:

1. set the knob  of your multimeter  to AC V
2. Choose the proper range .The numbers indicated in the multimeter are the maximum voltage reading for the range. 
3. Connect the test probe in the component being measured
4. Read the voltage value on the display

Using multimeter VOM as Ammeter

The DC ammeter- is used to measure the direct current of a circuit. The unit of measure is ampere (A). An multimeter can be used as ammeter by connecting it in series with the circuit. It requires correct application and polarity to measure the current.

Procedure:
1. Check the pointer of the meter if it set to zero
2. Set the knob at DC and set it to the desired ampere range.There are different ranges including 250 mA ,25mA 2.5mA and 50uA .For safety, set the knob at the top level (250mA ) to gain rough value when the current range is unknown. If you can not read it conveniently try to lower the range of the meter gradually in accordance with the first rough data for precise measurement.
3. Connect the test leads in series with the circuit. Apply the pin of the red lead to positive and black one to negative.
4. Read the current value in the display

Note

• Do not touch the test probe.
• Observe the polarity of the meter if the pointer deflects backward or the value to be negative,remove the connection immediately and reverse the connection of the test probe.