P 1.7-1 Conservation of energy requires that the sum of the power absorbed by all of the elements in a circuit be zero. Figure P 1.7-1 shows a circuit. All of the element voltages and currents are specified. Are these voltage and currents correct? Justify your answer.

 

Hint: Calculate the power absorbed by each element. Add up all of these powers. If the sum is zero, conservation of energy is satisfied and the voltages and currents are probably correct. If the sum is not zero, the element voltages and currents cannot be correct.

 

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Figure P 1.7-1

First identify the five elements.

All the elements are following the passive convention which means current as arrows are drawn are drawn so that current flows through the element from + terminal to – terminal.  That means, ordinarily power is lost, but if current or voltage are negative, then power could be being supplied.  So following hint, calculate power in each element and add to see if the total power is zero.

 

Element

-iV

P

A

-(2A)(-2V)

+4 W

 

 

 

B

-(2A)(5V)

-10 W

 

 

 

C

-(-5 A)(4 V)

+20 W

 

 

 

D

-(3 A)(3 V)

-9 W

 

 

 

E

-(5A)(1 V)

-5 W

 

 

 

Total

 

24 W – 24 W = 0

 

 

 

 

Since the total power sums to zero, the currents and voltages appear to be properly identified!

 

 

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This page last updated on December 26, 2018