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Unformatted text preview: CHAPTER 20 ELECTRIC CIRCUITS ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1. 1.5 A 2. (c) Ohms law states that the voltage V is directly proportional to the current I , according to V = IR , where R is the resistance. Thus, a plot of voltage versus current is a straight line that passes through the origin. 3. (e) Since both wires are made from the same material, the resistivity is the same for each. The resistance R is given by L R A = (Equation 20.3), where L is the length and A is the cross-sectional area of the wire. With twice the length and one-half the radius (one-fourth the cross-sectional area), the second wire has 2 8 1/ 4 L A = = times the resistance as the first wire. 4. 250 C 5. (a) Power P is the current I times the voltage V or P IV = (Equation 20.6a). However, since Ohms law applies to a resistance R , the power is also 2 P I R = (Equation 20.6b) and 2 V P R = (Equation 20.6c). Therefore, all three of the changes specified leave the power unchanged. 6. 27 W 7. 0.29 A 8. (d) According to Ohms law, the voltage across the resistance R 1 is 1 1 V IR = . The two resistors are connected in series, and their equivalent resistance is, therefore, R 1 + R 2 . According to Ohms law, the current in the circuit is 1 2 V I R R = + . Substituting this expression into the expression for V 1 gives 1 1 1 2 V V R R R = + . 30 ELECTRIC CIRCUITS 9. (b) The series connection has an equivalent resistance of S 2 R R R R = + = . The parallel connection has an equivalent resistance that can be determined from P 1 1 1 2 R R R R = + = . Therefore, it follows that 1 P 2 R R = . The ratio of these values is S 1 P 2 2 4 R R R R = = . 10. (e) Since the two resistors are connected in parallel across the battery terminals, the same voltage is applied to each. Thus, according to Ohms law, the current in each resistor is inversely proportional to the resistance, so that 1 1 2 2 2 1 / / I V R R I V R R = = . 11. 0.019 A 12. (c) In arrangement B the two resistors in series have a combined resistance of 2 R . Each series combination is in parallel, so that the reciprocal of the equivalent resistance is eq, B 1 1 1 1 2 2 R R R R = + = , or eq, B R R = . Following the technique outlined in Section 20.8, we also find that 3 eq, C 4 R R = and 2 eq, A 5 R R = . 13. (d) The internal resistance r of the battery and the resistance R are in series, so that the current from the battery can be calculated via Ohms law as V I R r = + . The voltage between the terminals is, then, 1 2 VR V IR R r = = + . This result can be solved to show that R = r . 14. (b) Kirchhoffs junction rule states that the sum of the magnitudes of the currents directed into a junction equals the sum of the magnitudes of the currents directed out of the junction....
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