Basic Algebra: tan δ = 1/wCR | Confirmation Needed

In summary, the equation tan δ = 1/wCR expresses the relationship between phase angle (δ), angular frequency (w), capacitance (C), and resistance (R) in AC circuits. It is commonly used to calculate the power factor and can be simplified by dividing both sides by wCR. To solve for a specific variable, basic algebraic principles can be applied. However, the equation has some limitations and may not accurately describe all circuit behaviors.
  • #1
rwooduk
762
59
please see attached image

why has our lecturer put tan δ = 1 / wCR ?

if you divide the two equations to get tan wouldn't it be R/wC ?

thanks for any conformation
 

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  • #2
if you divide the two equations to get tan wouldn't it be R/wC
... no.

Please show your working.
 
  • #3
Simon Bridge said:
... no.

Please show your working.

you're right, too much revision, can't think straight!

(-1/wc) / (R/1) = (-1/wc) * (1/R) = (-1/wRc)
 

Related to Basic Algebra: tan δ = 1/wCR | Confirmation Needed

1. What is the meaning of the equation tan δ = 1/wCR?

The equation tan δ = 1/wCR is an expression of the relationship between the phase angle (δ), angular frequency (w), capacitance (C), and resistance (R) in a basic algebraic form. It is commonly used in electrical engineering and physics to describe the behavior of AC circuits.

2. How is the equation tan δ = 1/wCR used in practical applications?

The equation tan δ = 1/wCR is used to calculate the power factor of an AC circuit. This is important in practical applications because it indicates the efficiency of the circuit and can help engineers optimize its performance.

3. Can the equation tan δ = 1/wCR be simplified further?

Yes, the equation can be simplified by dividing both sides by wCR, resulting in tan δ/wCR = 1. This form is often used in calculations as it is easier to work with.

4. How do I solve for a specific variable in the equation tan δ = 1/wCR?

To solve for a specific variable, you can rearrange the equation using basic algebraic principles. For example, if you want to solve for w, you would divide both sides by tan δ and then multiply by CR, resulting in w = 1/(tan δ x CR).

5. Are there any limitations to using the equation tan δ = 1/wCR?

The equation has some limitations, as it assumes ideal conditions and does not take into account factors such as inductance or frequency. In some cases, more complex equations may be needed to accurately describe the behavior of a circuit.

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