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Problem 1.10 Two electric circuits, represented by boxes A and B, are connected as shown in the figure. The reference direction for the current i in the interconnection and the reference polarity for the voltage v across the interconnection are as shown in the figure. Part A If I = 10A and v = 125V, Calculate the power in the interconnection. Express your answer to two significant figures and include the appropriate units. Solution: The current i is flowing from the negative to the positive terminal; thus, according to the passive sign convention, the power will be negative. Power = 125V * 10A = 1250 W and the sign of the power is negative. -‐1250W. To two significant figures, power = -‐1300W or -‐1.3kW. Part B State whether the power is flowing from A to B or vice versa. Solution: positive charges flow in the same direction as current. In this circuit, therefore, positive charges are flowing from negative to positive, thus gaining energy. As current flows through B then, charges are gaining energy (and power) and power is being delivered to A. Power is flowing from B to A Part C For I = 5A and v = -‐240V, calculate the power in the interconnection. Express your answer to two significant figures and include the appropriate units. Solution: Since v is negative, the terminals are reversed (the negative terminal is actually positive and the positive terminal is actually negative). Thus, the current is flowing from positive to negative terminals; positive charge is flowing from positive to negative terminals and energy is being lost through B (power is being delivered to B). Delivered power is positive. Power = 240* 5 = 1,200 W. To two significant figures, power = 1,200 W or 1.2kW Part D State whether the power is flowing from A to B or vice versa. Solution: since power is being delivered to B, power is flowing from A to B. Part E For i = -‐12A and v = 480V, calculate the power in the interconnection. Express your answer to two significant figures and include the appropriate units. Solution: The current is negative and is therefore flowing clockwise, rather than counter-‐clockwise through B. Thus, the current is flowing from positive to negative terminals in B; positive charge is flowing from positive to negative terminals and energy is being lost in or delivered to B. Delivered power is negative. Power = 12*480 = 5,760 W. To two significant figures, power = 5,800 W or 5.8kW Part F State whether the power is flowing from A to B or vice versa. Solution: since power is being delivered to B, power is flowing from A to B. Part G For I = -‐25A and v = -‐660V, calculate the power in the interconnection. Express your answer to two significant figures and include the appropriate units. Solution: Since v is negative, the terminals are reversed (the negative terminal is actually positive and the positive terminal is actually negative). The current is also negative and flowing clockwise, rather than counter-‐clockwise through B. Thus, the current is flowing from negative to positive terminals in B; positive charge is flowing from negative to positive terminals and energy is being generated by B. Generated power is negative. Power = 25*660 = -‐16,500 W. To two significant figures, power = -‐17,000 W or -‐17kW Part H State whether the power is flowing from A to B or vice versa. Solution: since power is being generated by B, power is flowing from B to A.
