To determine Find the total power developed in the circuit given in Figure P1.29. Explanation Given data: Refer to Figure P1.29 and Table P1.29 in the textbook. Calculation: The given circuit is redrawn as Figure 1. The positive sign should be used in power equation, if the reference direction of the current is in the direction of the reference voltage drop across the element. The negative sign should be used in power equation, if the reference direction of the current is in the direction of the reference voltage rise across the element. Such sign convention is called as Passive Sign Convention. For element “a”: The direction of the current is in the direction of voltage rise across the element. Therefore, the power equation should have the negative sign. Write the expression for power in element “a”. p a = − v a i a (1) Here, v a is the voltage across the element “a”, and i a is the current through the element “a”. Substitute − 18 V for v a and − 51 mA for i a in equation (1) to find p a . p a = − ( − 18 V ) ( − 51 mA ) = − ( − 18 ) ( − 51 × 10 − 3 ) V ⋅ A { ∵ 1 m = 10 − 3 } = − ( 918 × 10 − 3 ) W { ∵ 1 W = 1 V ⋅ 1 A } = − 918 mW { ∵ 1 m = 10 − 3 } For element “b”: The direction of the current is in the direction of voltage drop across the element. Therefore, the power equation should have the positive sign. Write the expression for power in element “b”. p b = v b i b (2) Here, v b is the voltage across the element “b”, and i b is the current through the element “b”. Substitute − 18 V for v b and 45 mA for i b in equation (2) to find p b . p b = ( − 18 V ) ( 45 mA ) = ( − 18 ) ( 45 × 10 − 3 ) V ⋅ A { ∵ 1 m = 10 − 3 } = − ( 810 × 10 − 3 ) W { ∵ 1 W = 1 V ⋅ 1 A } = − 810 mW { ∵ 1 m = 10 − 3 } For element “c”: The direction of the current is in the direction of voltage drop across the element. Therefore, the power equation should have the positive sign. Write the expression for power in element “c”. p c = v c i c (3) Here, v c is the voltage across the element “c”, and i c is the current through the element “c”. Substitute 2 V for v c and − 6 mA for i c in equation (3) to find p c . p c = ( 2 V ) ( − 6 mA ) = ( 2 ) ( − 6 × 10 − 3 ) V ⋅ A { ∵ 1 m = 10 − 3 } = − ( 12 × 10 − 3 ) W { ∵ 1 W = 1 V ⋅ 1 A } = − 12 mW { ∵ 1 m = 10 − 3 } For element “d”: The direction of the current is in the direction of voltage rise across the element. Therefore, the power equation should have the negative sign. Write the expression for power in element “d”. p d = − v d i d (4) Here, v d is the voltage across the element “d”, and i d is the current through the element “d”. Substitute 20 V for v d and − 20 mA for i d in equation (4) to find p d . p d = − ( 20 V ) ( − 20 mA ) = − ( 20 ) ( − 20 × 10 − 3 ) V ⋅ A { ∵ 1 m = 10 − 3 } = − ( − 400 × 10 − 3 ) W { ∵ 1 W = 1 V ⋅ 1 A } = 400 mW { ∵ 1 m = 10 − 3 } For element “e”: The direction of the current is in the direction of voltage rise across the element

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Chapter 1, Problem 29P

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Electric Circuits, Student Value Edition Format: Unbound (saleable)

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