2/5/20 Circuit Analysis Techniques • Equivalent resistance, R eq Voltage Divider Rule • Series and parallel resistors • Current divider and voltage divider & • Mesh and nodal analysis Current Divider Rule • Building on KVL and KCL • Review what we have done... EGR 220, Chapter 2 • Bring questions to office hours Feb 6, 2020 2 Recap Concepts Find R eq and I • Series Elements (draw example) • Exclusively share a single node and • Carry the same current. • Parallel Elements (draw example) • Share the same two nodes and • Have the same voltage drop across them. 3 4 1
2/5/20 Different R eq for Different Terminals We will discuss the role of V s and I s later (with Thevenin equivalent) 5 6 Voltage Divider Rule Re Resistors and elements in Se Series… • Current or voltage is the same for R 1 & R 2 ? • Current or voltage is partitioned across R 1 & R 2 ? • Prove, or demonstrate, using KCL and KVL. • 7 8 2
2/5/20 Voltage Divider: Series R Voltage Divider: Series R • Find v 1 , v 2 in terms of v src , R 1 & R 2 → • Solve for v 1 and v 2 derive the expression • Which resistor will have the larger V drop? 9 10 V-Divider Discussion Current Divider Rule • Re Resistors, elements and branches in Pa Parallel… • Current Divider: o I is partitioned, flowing through these resistors o What is the relationship of V for each element? o Prove, or demonstrate, using KCL and KVL. 11 12 3
2/5/20 Current Divider: Parallel R Current Divider: Parallel R • Find i 1 , i 2 in terms of i src , R 1 & R 2 • Solve for i 1 and i 2 • Derive the expression… • Which R will carry the larger current? i R 1 R 2 13 14 I -Divider Discussion Lab Experiments – Find R Multimeter (1) R = 10MΩ (2) R = 10kΩ 15 16 4
2/5/20 Lab Experiments – Find R Multimeter Lab Experiments – Find R Multimeter R = 10MΩ R = 10kΩ 17 18 Ammeter – Introduced Error Ammeter – Introduced Error • Find the current I in circuit (a). • An ammeter with an internal resistance of 1 W is inserted in the network to measure I ' as shown circuit (b). Does current, I ’ , increase or decrease relative to part (a)? 19 20 5
2/5/20 Voltmeter – Introduced Error Voltmeter – Introduced Error • Calculate the voltage V o in circuit (a). Is the voltage V ’ o , measured when a voltmeter with 6-k W • internal resistance is connected as in figure (b), greater or less than V o in circuit (a)? 21 22 Fundamental Analysis Tools for the Semester • Basic analysis laws • Ohm’s law • KVL: Kirchhoff’s voltage law Questions? • KCL: Kirchhoff’s current law • Analysis tools using the basic laws • Equivalent resistance • Current divider • Voltage divider • Mesh analysis • Nodal analysis • Equivalent Circuits 24 6
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