Ohms Law Conductance is the ability of an

Ohms Law ﻗﺎﻧﻮﻥ ﺍﻭﻡ • Conductance is the ability of an element to conduct electric current; it is the reciprocal of resistance R and is measured in mhos or siemens. • ﺍﻟﺘﻮﺻﻠﻴﺔ ﻫﻲ ﻗﺪﺭﺓ ﺍﻟﻌﻨﺼﺮ ﻋﻠﻰ ﺗﻮﺻﻴﻞ ﺍﻟﺘﻴﺎﺭ ﺍﻟﻜﻬﺮﺑﺎﺋﻲ ﻭ ﻫﻰ ﻋﻜﺲ ﺍﻟﻤﻘﺎﻭﻣﺔ (Siemens) • The power dissipated by a resistor: ﺍﻟﻘﺪﺭﺓ ﺍﻟﻤﺴﺘﻬﻠﻜﺔ ﻓﻲ ﺍﻟﻤﻘﺎﻭﻣﺔ 4

Nodes, Branches and Loops ﺍﻟﻌﻘﺪﺓ ﻭ ﺍﻟﻔﺮﻭﻉ ﻭ ﺍﻟﺪﻭﺍﺋﺮ • A branch represents a single element such as a voltage source or a resistor. ﻳﻤﺜﻞ ﺍﻟﻔﺮﻉ ﻋﻨﺼﺍ ﻭﺍﺣﺍ ﻣﺜﻞ . ﻣﺼﺪﺭ ﺍﻟﺠﻬﺪ ﺃﻮ ﺍﻟﻤﻘﺎﻭﻡ • A node is the point of connection between two or more branches. . ﺍﻟﻌﻘﺪﺓ ﻫﻲ ﻧﻘﻄﺔ ﺍﻻﺗﺼﺎﻝ ﺑﻴﻦ ﻓﺮﻋﻴﻦ ﺃﻮ ﺃﻜﺜﺮ • A loop is any closed path in a circuit. . ﺍﻟﺤﻠﻘﺔ ﻫﻲ ﺃﻲ ﻣﺴﺎﺭ ﻣﻐﻠﻖ ﻓﻲ ﺩﺍﺋﺮﺓ • A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology: 5

Nodes, Branches and Loops ﺍﻟﻌﻘﺪﺓ ﻭ ﺍﻟﻔﺮﻭﻉ ﻭ ﺍﻟﺪﻭﺍﺋﺮ Example 1 Original circuit Equivalent circuit How many branches, nodes and loops are there? 6

Kirchhoff’s ﻗﻮﺍﻧﻴﻦ ﻛﻴﺮﺷﻮﻑ ﻟﻠﺘﻴﺎﺭ current law (KCL) • Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero. ﻣﺠﻤﻮﻉ ﺍﻟﺘﻴﺎﺭﺍﺕ ﻓﻲ ﻧﻘﻄﺔ ) ﻋﻘﺪﺓ( ﻳﺴﺎﻭﻯ ﺻﻔﺮ Mathematically, 8

Kirchhoff’s ﻗﻮﺍﻧﻴﻦ ﻛﻴﺮﺷﻮﻑ ﻟﻠﺘﻴﺎﺭ current law (KCL) Example 4 I • ﺍﺣﺴﺐ ﻗﻴﻤﺔ ﺍﻟﺘﻴﺎﺭ I + 4 -(-3)-2 = 0 ÞI = -5 A We can consider the whole enclosed area as one “node”. This indicates that the actual current for I is flowing in the opposite direction. 9

Kirchhoff’s ﻗﻮﺍﻧﻴﻦ ﻛﻴﺮﺷﻮﻑ ﻟﻠﺘﻴﺎﺭ voltage law (KVL) • Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero. ﻣﺠﻤﻮﻉ ﺍﻟﺠﻬﻮﺩ ﻓﻲ ﺩﺍﺋﺮﺓ ﻣﻐﻠﻘﺔ ﻳﺴﺎﻭﻯ ﺻﻔﺮ Mathematically, 10

Series Resistors and Voltage Division ﺍﻟﻤﻘﺎﻭﻣﺎﺕ ﺍﻟﻤﺘﺼﻠﺔ ﺑﺎﻟﺘﺴﻠﺴﻞ ﻭ ﻣﻘﺴﻢ ﺍﻟﺠﻬﺪ • Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current. ���� �������� ���� • The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances. ﺍﻟﻤﻘﺎﻭﻣﺔ ﺍﻟﻤﻜﺎﻓﺌﺔ ﻟﻠﻤﻘﺎﻭﻣﺎﺕ ﺍﻟﻤﺘﺼﻠﺔ ﻋﻠﻰ ﺍﻟﺘﺴﻠﺴﻞ ﻫﻮ ﺍﻟﻤﺠﻤﻮﻉ ﺍﻟﺠﺒﺮﻯ ﻟﻠﻤﺠﻤﻮﻉ ﻗﻴﻤﻬﺎ • The voltage divider can be expressed as �� ������ 12

Parallel Resistors and Current Division ﺍﻟﻤﻘﺎﻭﻣﺎﺕ ﺍﻟﻤﺘﺼﻠﺔ ﺑﺎﻟﺘﻮﺍﺯﻯ ﻭ ﻣﻘﺴﻢ ﺍﻟﺘﻴﺎﺭ • Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them. ����� �������� ���� • The equivalent resistance of a circuit with N resistors in parallel is: ﺍﻟﻤﻘﺎﻭﻣﺔ ﺍﻟﻤﻜﺎﻓﺌﺔ ﻟﻠﻤﻘﺎﻭﻣﺎﺕ ﺍﻟﻤﺘﺼﻠﺔ ﻋﻠﻰ ﺍﻟﺘﻮﺍﺯﻱ ﻳﻌﻄﻰ ﺑﺎﻟﻌﻼﻗﺔ • The total current i is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as: �� ���� 14

Parallel Resistors and Current Division ﺍﻟﻤﻘﺎﻭﻣﺎﺕ ﺍﻟﻤﺘﺼﻠﺔ ﺑﺎﻟﺘﻮﺍﺯﻯ ﻭ ﻣﻘﺴﻢ ﺍﻟﺘﻴﺎﺭ Example 4 2 W, 3 W and 2 A are in parallel 15

Wye-Delta Transformations ﺍﻟﺘﺤﻮﻳﻞ ﻣﻦ Y-Δ

Wye-Delta Transformations ﺍﻟﺘﺤﻮﻳﻞ ﻣﻦ Y-Δ Delta -> Star -> Delta 17

Wye-Delta Transformations ﺍﻟﺘﺤﻮﻳﻞ ﻣﻦ Y-Δ

Wye-Delta Transformations