How Do You Calculate Resistance and Inductance in a Single Phase A.C. Coil?

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In summary: This means that the total voltage at any point is the sum of the voltage across R and the voltage across L.In summary, the coil has a resistance of 16.26Ω and an inductance of 0.052H.
  • #1
Physicist3
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1. A coil connected to a 230V 50Hz supply takes a current of 10A at a phase angle of 30o Calculate the resistance and inductance of the coil



2. i = ImSinωt, R=V/I and XL=2∏fL



3. To get the resistance I used the value of 10A to get the value of Imby dividing 10 by sin30 which = 20A. I then multiplied this by 0.707 to get RMS value as I believe the Voltage to be RMS as well. I then divided voltage by current to get resistance of 16.26Ω but the answer in the book says 21.65Ω and I can't seem to get this value. For the inductance I divided voltage by current again to get XL which I get as 16.26 again. I then divided this by 2∏ x 50 to get a value of 0.052H but the book says 39.8mH and I can't seem to work out how to get to the answers in the book
 
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  • #2
Model it by a series circuit: R and L. Of the 230V applied, use trig to determine how much voltage appears across the R and how much across Ѡ.L

You know the current in each series element is 10A.

Parameters are already in RMS, so no further conversion is needed.
 
  • #3
Sorry but am I missing something because I am really struggling as how to find how much voltage is in each element if I've been given a source voltage, frequency and current?
 
  • #4
Physicist3 said:
Sorry but am I missing something because I am really struggling as how to find how much voltage is in each element if I've been given a source voltage, frequency and current?

You are also told the power-factor angle, so ...

You draw a right-angled triangle showing how the voltage across R adds to the voltage across L to produce 230V. Mark in the angle whose value you know.
 
  • #5
Explaining further: because the elements are in series, it is convenient that we take the current as reference, because that current is common to each element (it's identical in each element at all times). The voltage across the R is in phase with this current, (it always is for a resistor) so you can draw the voltage phasor as being parallel to the current phasor. The voltage across the L is 90 degrees ahead of the current, so you can draw the inductor's voltage phasor as 90 degrees ahead of the current.
 

FAQ: How Do You Calculate Resistance and Inductance in a Single Phase A.C. Coil?

What is a single phase A.C. coil?

A single phase A.C. coil is a type of electrical coil that is used in alternating current (A.C.) circuits to convert the incoming electrical energy into a magnetic field. It is typically made up of a wire wound around a core, and is used in various electronic devices such as transformers, motors, and generators.

How does a single phase A.C. coil work?

A single phase A.C. coil works by utilizing the principles of electromagnetism. When an alternating current flows through the coil, it creates a changing magnetic field which induces a voltage in the coil. This voltage can then be used to power other electrical components in a circuit.

What are the applications of single phase A.C. coils?

Single phase A.C. coils have a wide range of applications in the field of electrical engineering. They are commonly used in power transmission and distribution systems, as well as in various electronic devices such as transformers, motors, and generators.

How is a single phase A.C. coil different from a three phase A.C. coil?

The main difference between a single phase A.C. coil and a three phase A.C. coil is the number of phases in the electrical circuit. A single phase A.C. coil has only one phase, while a three phase A.C. coil has three phases. This affects the way the coils are wired and the type of load they can handle.

How can I determine the voltage and current rating of a single phase A.C. coil?

The voltage and current rating of a single phase A.C. coil can be determined by checking its specifications or by using a multimeter to measure the voltage and current in the circuit. It is important to ensure that the coil can handle the required voltage and current to avoid damage or malfunction.

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