To determine Show that the power balances in the circuit given in Figure 1.7. Explanation Given data: Refer to Figure 1.7 and Table 1.5 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 drop across the element. Therefore, the power equation should have the positive 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 120 V for v a and − 10 A for i a in equation (1) to find p a . p a = ( 120 V ) ( − 10 A ) = − ( 120 ) ( 10 ) V ⋅ A = − 1200 W { ∵ 1 W = 1 V ⋅ 1 A } For element “b”: 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 “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 120 V for v b and 9 A for i b in equation (2) to find p b . p b = − ( 120 V ) ( 9 A ) = − ( 120 ) ( 9 ) V ⋅ A = − 1080 W { ∵ 1 W = 1 V ⋅ 1 A } 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 10 V for v c and 10 A for i c in equation (3) to find p c . p c = ( 10 V ) ( 10 A ) = ( 10 ) ( 10 ) V ⋅ A = 100 W { ∵ 1 W = 1 V ⋅ 1 A } 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 10 V for v d and − 1 A for i d in equation (4) to find p d . p d = − ( 10 V ) ( − 1 A ) = ( 10 ) ( 1 ) V ⋅ A = 10 W { ∵ 1 W = 1 V ⋅ 1 A } For element “e”: 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 “e”. p e = v e i e (5) Here, v e is the voltage across the element “e”, and i e is the current through the element “e”. Substitute − 10 V for v e and − 9 A for i e in equation (5) to find p e . p e = ( − 10 V ) ( − 9 A ) = ( 10 ) ( 9 ) V ⋅ A = 90 W { ∵ 1 W = 1 V ⋅ 1 A } For element “f”: The direction of the current is in the direction of voltage rise across the element

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ISBN: 9781292060545

Author: James W. Nilsson, Susan Riedel

Publisher: Pearson Education Limited

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Chapter 1, Problem 34P

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Show that the power balances in the circuit given in Figure 1.7.

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