Overlay method

The overlay method is a method of calculating electric circuits, based on the assumption that the electric current in each branch of the electric circuit with all the generators turned on is equal to the sum of the currents in the same branch obtained when each of the generators is turned on in turn and the other generators are turned off (only in linear circuits )

The overlay method is used both for the calculation of DC circuits and for the calculation of AC circuits.

Application example

Find current $I_{1}$ ${\ displaystyle I_ {1}}$ overlay in the circuit shown in the figure. $E_{1}=100B$ ${\ displaystyle E_ {1} = 100B}$ , $E_{2}=50B$ ${\ displaystyle E_ {2} = 50B}$ , $R_{1}=R_{2}=R_{3}=10$ ${\ displaystyle R_ {1} = R_ {2} = R_ {3} = 10}$ ${\text{Ом}}$ ${\ displaystyle {\ text {Ohm}}}$ .

Blend Method Example

When generator 2 is off, current $I_{1}'$ ${\ displaystyle I_ {1} '}$ we find by the formula:

I_{1}'={\frac {E_{1}}{R_{1}+{\frac {R_{2}R_{3}}{R_{2}+R_{3}}}}}={\frac {100}{10+{\frac {10\cdot 10}{10+10}}}}=6,67A

{\ displaystyle I_ {1} '= {\ frac {E_ {1}} {R_ {1} + {\ frac {R_ {2} R_ {3}} {R_ {2} + R_ {3}}}} } = {\ frac {100} {10 + {\ frac {10 \ cdot 10} {10 + 10}}}} = 6.67A}

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With the source turned off, 1 current $I_{2}''$ ${\ displaystyle I_ {2} ''}$ will be

I_{2}''={\frac {E_{2}}{R_{2}+{\frac {R_{1}R_{3}}{R_{1}+R_{3}}}}}={\frac {50}{10+{\frac {10\cdot 10}{10+10}}}}=3,34A

{\ displaystyle I_ {2} '' = {\ frac {E_ {2}} {R_ {2} + {\ frac {R_ {1} R_ {3}} {R_ {1} + R_ {3}}} }} = {\ frac {50} {10 + {\ frac {10 \ cdot 10} {10 + 10}}}} = 3.34A}

,

and current $I_{1}''$ ${\ displaystyle I_ {1} ''}$ will be

I_{1}''=-{\frac {I_{2}''}{2}}=-{\frac {3,34}{2}}=-1,67A

{\ displaystyle I_ {1} '' = - {\ frac {I_ {2} ''} {2}} = - {\ frac {3.34} {2}} = - 1.67A}

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Then current $I_{1}$ ${\ displaystyle I_ {1}}$ with both sources turned on it will be equal to the sum of currents $I_{1}'$ ${\ displaystyle I_ {1} '}$ and $I_{1}''$ ${\ displaystyle I_ {1} ''}$ :

I_{1}=I_{1}'+I_{1}''=6,67-1,67=5A

{\ displaystyle I_ {1} = I_ {1} '+ I_ {1}' '' = 6.67-1.67 = 5A}

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In the problem for positive current directions $I_{1}'$ ${\ displaystyle I_ {1} '}$ and $I_{1}''$ ${\ displaystyle I_ {1} ''}$ Directions coinciding with the direction shown in the figure for current $I_{1}$ ${\ displaystyle I_ {1}}$ . Same for current $I_{2}''$ ${\ displaystyle I_ {2} ''}$

Literature

Bessonov L.A. Theoretical foundations of electrical engineering. Electrical circuits. - M .: Gardariki, 2002 .-- 638 p. - ISBN 5-8297-0026-3 .

Overlay method

Application example

Literature

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