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Chapter 27

# Chapter 27 - equation will come from Junction rule at point...

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EXAM 2 Wednesday, Feb 27 th Chapters 25, 26, and 27

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Multiloop Circuits - Kirchhoff's Rules The sum of the currents entering any junction is equal to the sum of the currents leaving the junction. Kirchhoff's Junction Rule : The algebraic sum of the changes in potential encountered in a complete traversal of any loop in a circuit is equal to zero. Kirchhoff's Loop Rule :
R i motion - V iR = R i motion V iR = + motion - V = E + - motion V = + E + - For a move through a resistance in the direction of the current, the change in the potential is For a move through a resistance in the direction opposite to that of the current . V iR = - Resistance Rule : , the change in the potential is . V iR = + For a move through an ideal emf device in the direction of the emf arrow, the change in the potential is For a move through an ideal emf device in a direction opposite to th at of th . V = + EMF Rule : . E e emf arrow, the change in the potential . s i V = - . E

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1 2 3 1 3 2 In order to determine the currents , , and in the circuit we need three equations. The first
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Unformatted text preview: equation will come from Junction rule at point : Junction d: ( ) i i i d i i i + = eq. 1 1 1 1 3 3 The other two will come from Loop Rule: If we traverse the left loop ( ) starting at and going in the counterclockwise direction we get: Loop : 0 ( ). Now we go around the ri bad b bad i R i R-+ = eq. 2 E 3 3 2 2 2 1 2 ght loop ( ) starting at point and going in the counterclockwise direction: Loop : 0 ( ) We have a system of three equations (eqs.1, 2, and 3) and three unknowns , , and bcd b bcd i R i R i i---= eq. 3 E ( 29 3 . If a numerical value for a particular current is negative, this means that the chosen direction for this current is wrong and that the current flows in the opposite direction. We can write a fourth i 1 1 1 2 2 2 equation (Loop rule for the outer loop ) but this equation does not provide any new information. Loop : 0 ( ) abcd abcd i R i R---= eq. 4 E E...
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