CH2_Problems - 1 08 C hapter 2 Resistive Circuits P roblems...

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108 Chapter 2 Resistive Circuits Problems Section 2.1: Resistances in Series and Parallel *P2.1. Reduce each of the networks shown in Figure P2.1 to a single equivalent resistance by com- bining resistances in series and parallel. 3Q 3Q 30Q 12Q 24Q 7Q 4Q (a) lOQ 6Q 24Q 1s n 60Q 9Q sn 6Q (b) Figure P2.1 *P2.2. A 4-Q resistance is in series with the paral- lel combination of a 20-Q resistance and an unknown resistance Rx. The equivalent resis- tance for the network is 8 Q. Determine the value of Rx. *P2.3. Find the equivalent resistance looking into terminals a and bin Figure P2.3. Figure P2.3 *P2.4. Suppose that we need a resistance of 1.5 kQ and you have a box of 1-kQ resistors. Devise a network of 1-kQ resistors so the equivalent resistance is 1.5 kQ. Repeat for an equivalent resistance of 2.2 kQ. *P2.5. Find the equivalent resistance between ter- minals a and bin Figure P2.5. 4Q Figure P2.5 P2.6. Find the equivalent resistance between termi- nals a and b for each of the networks shown in Figure P2.6. b 16!2 4Q 6Q 20!2 180 6Q 1s n (a) 4Q 6Q a b sn 3n (b) Figure P2.6 63!2 * Denotes that answers are contained in the Student Solutions files. See Appendix F for more information about accessing the Student Solutions.
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4Q 30Q 24Q 6Q 20Q (c) Figure P2.6 (Cont.) P2.7. What resistance in parallel with 120 Q results in an equivalent resistance of 48 Q? P2.8. a. Determine the resistance between termi- nals a and b for the network shown in Figure P2.8. b. Repeat after connecting c and d with a short circuit. ao------i 6Q ---------{) c bo-- ----- Figure P2.8 P2.9. Two resistances having values of R and 2R are in parallel. R and the equivalent resis- tance are both integers. What are the possible values for R? P2.10. A network connected between terminals a and b consists of two parallel combinations that are in series. Th e first parallel combi- nation is compo sed of a 16-Q resistor and a 48-Q resistor. The se cond parallel combina- tion is composed of a 12-Q resistor and a 24-Q resistor. Draw the network and determine its equivalent resistance. P2.11. Two resistances R1 and R2 are connected in parallel. We know that R1 = 90 Q and that the current through R2 is three times the value of the current through R1. Determine the value of R2. P2.12. Find the equivalent resistance for the infi- nite network shown in Figure P2.12(a). Becau se of its form, this network is called a semi-infinite ladder. (Hint: If another Problems 1 09 section is added to the ladder as shown in Figure P2.12(b ), the equivalent resistance is the same. Thus , working from Figure P2.12(b ), we can write an expression for R eq in terms of Req. Then, we can solve for Req.) JQ JQ > lQ JQ JQ 2Q 2Q JQ (a) (b) Figure P2.12 JQ 2Q JQ Ladder network of (a) • • • P2.13. If we connect n 1000-Q resistances in parallel, what value is the equivalent resistance? P2.14. The heating element of an electric cook top has two resistive elements, R1 = 57.6 Q and R2 = 115.2 Q, that can be operated separately, in series, or in parallel from volt- ages of either 120 V or 240 V. For the low- est power, R1 is in series with R 2, and the combination is operated from 120V. What is the lowest power? For the highest power, how should the elements be operated? What
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