Inductance: Can L1 and L2 be replaced by an equivalent inductor in Figure 4(b)?

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In summary, we can replace inductors L1 and L2 with an equivalent inductor Leq, where Leq = L1L2-M^2/L1+L2-2M. This can be seen by solving for Leq in the given equation and substituting it into the expression for V/jω, resulting in V/jω*Leq = L1*L2-M^2/L1+L2-2M. It was determined in a Physics Forums thread that this solution is correct.
  • #1
james123

Homework Statement



(c) See if you can show that L1 and L2 can be replaced by the

equivalent inductor, Leq, of FIGURE 4(b) where Leq = L1L2-M^2/L1+L2-2M

Homework Equations

The Attempt at a Solution


[/B]
I+I1+I2

Leq = V(L2-M)/jω(L1*L2-M^2) + V(L1-M)/jω(L1*L2-M^2)

= V*(L1+L2)-2M/jω(L1*L2-M^2)

V/jω*Leq = L1*L2-M^2/L1+L2-2M

Can anybody tell me if I'm close with this one or not? Struggling for days with it!

Any advice is appreciated!
 
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  • #3
Ahh great! So after reading through I presume 'his_tonyness' got part 'C' correct since he wasn't corrected by yourself apart from I=I1+I2?
 
  • #4
james123 said:
Ahh great! So after reading through I presume 'his_tonyness' got part 'C' correct since he wasn't corrected by yourself apart from I=I1+I2?
I believe that is the case. It's been a while since I took part in that thread (2015).
 
  • #5
Many thanks gneill!
 

FAQ: Inductance: Can L1 and L2 be replaced by an equivalent inductor in Figure 4(b)?

1. What is inductance and how does it work?

Inductance is the property of an electrical circuit that causes an opposing voltage to be induced in response to a change in current. It works by storing energy in the form of a magnetic field and releasing it when the current changes.

2. How is inductance measured and what are its units?

Inductance is measured in units called henries (H) and can be measured using a device called an inductance meter. The unit is named after the scientist Joseph Henry who discovered inductance.

3. What factors affect the inductance of a circuit?

The inductance of a circuit is affected by the number of turns in the wire, the material of the core, and the size and shape of the core. It also depends on the frequency of the current and the presence of other nearby conductors.

4. What are some real-life applications of inductance?

Inductance has many practical applications, including in transformers, motors, generators, and electronic components such as inductors and chokes. It is also used in wireless charging, energy storage, and inductive heating.

5. How does inductance differ from capacitance?

Inductance and capacitance are two fundamental properties of electrical circuits that are inversely related to each other. Inductance is the ability to store energy in a magnetic field, while capacitance is the ability to store energy in an electric field. They both affect the flow of current in a circuit, but in different ways.

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