Understanding Resistive Circuits: Ohm's Law, Kirchhoff's Laws, and More

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Explore resistive circuits in detail with topics such as Ohm's Law, Kirchhoff's Laws, resistor types, power absorption, examples, glossary definitions, and more. Learn about nodes, loops, branches, and how to apply Kirchhoff's current and voltage laws in circuit analysis. Enhance your understanding of resistive materials, current flow, power calculations, and circuit components.

  • Resistive circuits
  • Ohms Law
  • Kirchhoffs Laws
  • Resistor types
  • Circuit analysis
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  1. 1 Chapter 2. Resistive circuits EMLAB

  2. Contents 2 1. Ohm s law 2. Kirchhoff s laws 3. Series and parallel resistor combinations 4. Y- transformation 5. Circuits with dependent sources EMLAB

  3. Resistors : microscopic view 3 nucleus electrons Entering resistive material, charges are decelerated, which decrease current flow. EMLAB

  4. Types of resistors 4 (1), (2), and (3) are high power resistors. (4) and (5) are high-wattage fixed resistors. (6) is a high precision resistor. (7) (12) are fixed resistors with different power ratings. EMLAB

  5. 1. Ohms law 5 resistance ?(?) = ?(?) ? (? 0) ? 1 ; conductance ? ?(?) = ?(?) ?(?) = ?2? =?2 Power absorption : ? EMLAB

  6. Example 2.1 6 Determine the current and the power absorbed by the resistor. ? =12 2?= 6 [??] ? = ?? = (12)(6 10 3) = 0.072 [?] = ?2? = (6 10 3)2(2?) = ?2/? = (12)2/2? EMLAB

  7. Glossary 7 (1) Node A node is simply a point of connection of two or more circuit elements. node Although one node can be spread out with perfect conductors, it is still only one node EMLAB

  8. 8 (2) loop A loop is simply any closed path through the circuit in which no node is encountered more than once (3) branch a branch is a single or group of components such as resistors or a source which are connected between two nodes EMLAB

  9. 2. Kirchhoffs law 9 (1) Kirchhoff s current law (KCL) : the algebraic sum of the currents entering(out-going) any node is zero the sum of incoming currents is equal to the sum of outgoing currents. File:Kirchhoff's first law example.png ?1+ ?2+ ( ?3) + ( ?4) + ( ?5) = 0 ?1+ ?2= ?3+ ?4+ ?5 (2) Kirchhoff s voltage law (KVL), the algebraic sum of the voltages around any loop is zero EMLAB

  10. Kirchhoffs Current law 10 ??(?) = 0 ? ?2(?) ?1(?) ??(?) = ?1(?) + ?2(?) + ?3(?) = 0 ?1(?) ?2(?) ?0(?) ? ?1(?) =?0 ?1 ?2(?) =?0 ?2 ?3(?) =?0 ?3 , , R2 R1 ?1 ?2 ?3 ?3(?) R3 ?0 ?1 ?1 +?0 ?2 ?2 +?0 ?3 ?3 = 0 ?3(?) Current definition The direction of a current can be chosen arbitrarily. R ?? The value of a current can be obtained from a voltage drop along the direction of current divided by a resistance met. ?? ? ?? ?? ? EMLAB

  11. Kirchhoffs Voltage law 11 ??(?) = 0 ? Sum of voltage drops along a closed loop should be equal to zero! ?1(?) + ?2(?) ??(?) = 0 +?1(t) +?2(t) C1 R1 Voltage convention ???= ?? ?? + ??(t) EMLAB

  12. Example 2.6 12 Find the unknown currents in the network. Node 1 : ?1 60? 20? = 0 Node 2 : ?4 ?1 ?6= 0 Node 3 : ?4+ ?5+ 60? 40? = 0 Node 4 : ?5+ 20? + 30? = 0 Node 5 : ?6+ 40? 30? = 0 ?4= 70[??] ?1= 80[??] ?5= 50[??] ?6= 10[??] EMLAB

  13. Example E2.6 13 Find the current ixin the circuits in the figure. ??+ 10?? 120? + 12? = 0 ??+ 10?? 44? = 0 ??= 4[??] ??= 12[??] EMLAB

  14. Example E2.8 14 Find Vadand Vebin the network in the figure. ???= 24 4 + 6 = 26[?] ???= 8 6 + 24 = 10[?] EMLAB

  15. Example 2.15 15 Given the following circuit, let us find I, Vbdand the power absorbed by the 30k resistor. Finally, let us use voltage division to find Vbc. 20? 6 + ? 10? + ? 20? + 12 + ? 30? = 0 ???= 20? + 40? ( 6) = 2[?] 6 ? = 60?= 0.1[??] ???= ? 20? + 12 = 2 + 12 = 10 [?] ?30?= ?2 30? = 0.01 10 6 30? = 0.3 [??] EMLAB

  16. Series resistors 16 equivalent ??= ?1+ ?2+ + ?? EMLAB

  17. Parallel resistors 17 equivalent 1 1 ?1 1 ?2 1 = + + + ?? ?? EMLAB

  18. Example 2.19 18 Given the circuit, we wish to find the current in the 12-k load resistor. equivalent 1 1 12? ??= ( 1?) = 3 + 1 ( 1?) 1 1 4?+ 12? = 0.25 [??] EMLAB

  19. Example 2.20 19 We wish to determine the resistance at terminals A-B in the network in the figure. EMLAB

  20. Y-transformation 20 Y equivalent ?1?2 ?1=????+ ????+ ???? ??+ ??=?2(?1+ ?3) ?1+ ?2+ ?3 ??= ?1+ ?2+ ?3 ?2?3 ?1+ ?2+ ?3 ?3?1 ?1+ ?2+ ?3 ? ?? ?2=????+ ????+ ???? ??= ?? ?3=????+ ????+ ???? ??+ ??=?3(?1+ ?2) ?1+ ?2+ ?3 ??= ?? ? ??+ ??=?1(?2+ ?3) ?1+ ?2+ ?3 ??=? ? = ?1= ?2= ?3 3 EMLAB

  21. 21 ?1 ?2+ ?3 = ??+ ?? (1) ?2 ?1+ ?3 = ??+ ?? (2) ?3 ?1+ ?2 = ??+ ?? (3) 1 2 + 3 = 2?? EMLAB

  22. Example 2.26 22 Given the network in Fig. 2.36a, let us find the source current IS. 12? 18? 12? + 18? + 6?= 6 [? ] 12? 6? 12? + 6?= 4 [? ] ??= ??= 18? 6? 12? + 18? + 6?= 3 [? ] 12 ??= ??= 6? + 4?= 1.2 [??] 12? 6? 12? + 18? + 6?= 2 [? ] ??= EMLAB

  23. 2.8 Circuits with dependent sources 23 Example 2.27 Let us determine the voltage Voin the circuit in the figure. 12 + ?1 3? 2000 ?1+ ?1 5? = 0 12 ?1= 3? 2? + 5?= 2 [??] ?0= ?1 5? = 10 [?] EMLAB

  24. Example 2.28 24 Given the circuit in the figure containing a current-controlled current source, let us find the voltage Vo. 10? +?? ?0=?? 6?+ ?0 4?0= 0, 3? 10? +?? 6? ?? 1?= 0 60 5??= 0 ??= 12 [?], ?0= 8 [?] EMLAB

  25. Example 2.30 25 An equivalent circuit for a FET common-source amplifier or BJT common-emitter amplifier can be modeled by the circuit shown in the figure. We wish to determine an expression for the gain of the amplifier, which is the ratio of the output voltage to the input voltage. GND can be arbitrarily set. 0 ? ??= ?3||?4||?5 ??+ ?1?1+ ?1?2= 0 0 ? ?0= ?????? ?2 ??= ?? ?1+ ?2 = ?????? ?(????) =?0 ?2 = ???? ?? ?? ?1+ ?2 EMLAB

  26. Transistor amplifier 26 Transistor EMLAB

  27. 2.10 Application examples 27 Example 2.33 : The Wheatstone bridge circuit. ?3 ?? ?1 ?3 =?2 ?? = ?1+ ?3 ?2+ ?? ?3 ?1 ??= ?2 EMLAB

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