Magnetic Coupled Circuit problem

[lazyaditya]

Q. In figure shown,if i₁(t)=2tu(t) A,a voltage V_CD =10u(t)mV is observed,then the placements of the dots and the value of mutual inductance M is what ?

Sine current is entering the primary winding so i place a dot at "A",but where should put a dot in secondary winding.I do know that according to the lenz's law emf should be induced in secondary winding so as to oppose the cause of induced emf.

 

[lazyaditya]

I think i should put a dot at "C" since the voltages V_AB and V_CD are in phase thus sense of winding will be at same position for both the windings,that will be at top.

 

[gneill]

Placing a single dot on one inductor does not solve the problem. The dots work in pairs, defining the relative phase or sense of the turns (wrapping direction) of the windings.

The rule of thumb is that a current flowing into the dot on one conductor will cause a current to flow out of the dot on its coupled partner. So that means the voltage produced across the winding must be conducive to making that current direction happen. You're given the current for the primary and the resulting voltage on the secondary...

Note also that with the dots correctly placed you could swap all the dots to the other ends of their inductors and have another correct solution.

 

[lazyaditya]

Why it will cause current to flow out of the dot on the coupled coil.

 

[lazyaditya]

Oh the current is taken outward so that flux due to both the currents must be additive. Am I correct ?

 

[gneill]

The current is caused by the changing magnetic flux. The dots are simply indicators to tell you what polarity of event will happen at one inductor if the current changes through another one. The convention is that an increase in current into the dot on one inductor will result in a current flowing out of the dot on the coupled inductor.

In one inductor a changing current means a changing magnetic flux. A portion of this changing flux is coupled to the other coil (mutual inductance) where a potential is induced and current made to flow. The dots tell you what polarity the induced EMF will be and the direction of the current that results given an increase in current into the dot on the other coil.

 

[lazyaditya]

I am sorry but i am still not comfortable with this concept. How does dot tells what polarity the induced emf will be ?

 

[gneill]

I am sorry but i am still not comfortable with this concept. How does dot tells what polarity the induced emf will be ?

An increasing current flowing INTO the dot on one inductor will cause an increasing current to flow OUT of the dot on the other inductor. If the current is flowing out of the dot the induced EMF must make that happen (so the load will draw that current).

Think of a schematic of a simple transformer with a resistive load on the secondary. The dots happen to be placed at the top of each winding. Increasing current flowing into the top of the primary will cause increasing current to flow out of the top of the secondary. So what polarity of potential drop occurs across the load? What does that tell you about the polarity of the EMF induced on the secondary?

 

[lazyaditya]

Polarity of emf induced on secondary will be positive at top .

 

[gneill]

Polarity of emf induced on secondary will be positive at top .

Yup! :)

 

[lazyaditya]

So I will put one dot at "A" and the other dot at "C" so that polarity at point A and polarity at point C remains in phase.