Circuit analysis (with transformers and motor)

In summary, the conversation discusses the calculation of the impedance and source current for a motor arrangement using ideal transformers and lossless transmission lines. The motor is loaded to deliver 5hp with a power factor of 0.6 lagging and an efficiency of 90%. The impedance of the normally running motor is found to be 8.34Ω and the impedance seen by the source Es is 2.32mΩ. The source current is not mentioned. The speaker also expresses the need for help with the calculations due to the motor's efficiency.
  • #1
sandy.bridge
798
1

Homework Statement


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Consider the motor arrangement shown, Assume ideal transformers and lossless transmission lines. The start capacitor shown in series with the motor is only used to start the motor, and is then shorted out of the circuit. The motor is loaded such that it delivers 5hp, and has a power factor of 0.6 lagging, and the motors efficiency is 90%.

A)Find the impedence of the normally running motor (ie. capacitor shorted).
[tex]P_{out}=5hp=3730W, P_{in}=3730W/0.9=4144W, F_P=0.6[/tex]
[tex]Z=V^2/S[/tex]
[tex]S=\sqrt{Q^2+P_{in}^2}=\sqrt{(tan(cos^{-1}(F_P))P_{in})^2+P_{in}^2}= \sqrt{(tan(cos^{-1}(0.6))4144W)^2+(4144W)^2}=6907VAR [/tex]
and
[tex]Z=(240V)^2/6907VAR=8.34Ω [/tex]

B) What impedence is seen by the source Es? What is the magnitude of the source current?
Firstly, I considered the motor segment to be "secondary".
[tex]Z_S=n^2Z_P,\rightarrow{Z}_P=Z_S(e_2/e_p)^2=(8.34Ω)(240V/14.4(10)^3V)^2=2.32mΩ [/tex]
 
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  • #2
I don't really think I did the calculation of the impedence in part A correctly. Since the motor is 90% efficient, that indicates that 10% of its input energy is dissipated within its terminals due to internal impedence. I would really appreciate some help with this question, as I cannot move on without it! Thanks
 

Related to Circuit analysis (with transformers and motor)

1. What is a transformer and how does it work?

A transformer is a device used in electrical circuits to change the voltage level of an alternating current (AC). It consists of two coils of wire, called the primary and secondary winding, wrapped around a core made of ferromagnetic material. When an AC current flows through the primary winding, it creates a magnetic field in the core which induces a voltage in the secondary winding. This allows for the efficient transfer of electrical energy between circuits with different voltage levels.

2. How do I calculate the voltage and current in a circuit with a transformer?

To calculate the voltage and current in a circuit with a transformer, you will need to use the transformer equation, which states that the ratio of the primary and secondary voltages is equal to the ratio of the number of turns in the windings. This can be written as Vp/Vs = Np/Ns, where Vp and Vs are the primary and secondary voltages, and Np and Ns are the number of turns in the primary and secondary windings, respectively. Similarly, the current ratio can be calculated using the same equation.

3. What is the purpose of a motor in a circuit?

A motor is a device that converts electrical energy into mechanical energy. In a circuit, a motor is used to provide rotational motion, which can be harnessed for various applications such as moving machinery, vehicles, or household appliances. It works by using the principle of electromagnetic induction, where a current-carrying coil experiences a force when placed in a magnetic field, causing it to rotate.

4. How do I analyze a circuit with a transformer and motor?

To analyze a circuit with a transformer and motor, you can use the laws of circuit analysis, such as Kirchhoff's laws, Ohm's law, and the transformer equation. First, you will need to determine the equivalent circuit with the transformer and motor included. Then, you can use these laws to calculate the voltage, current, and power in each component of the circuit. It is also important to consider the efficiency and power loss in the transformer and motor when analyzing the circuit.

5. What are the safety precautions when working with circuits containing transformers and motors?

When working with circuits containing transformers and motors, it is important to follow proper safety precautions to prevent electric shock and other hazards. This includes wearing appropriate personal protective equipment, keeping the circuit de-energized when not in use, and properly grounding the circuit. It is also important to be aware of the risks associated with high voltages and currents, and to handle all components with caution. If unsure, it is best to seek guidance from a trained professional.

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