Consider the following circuit containing two sources with internal resistance a

Question

Consider the following circuit containing two sources with internal resistance and two load resistors. a. How much current flows through this circuit and in what direction does it flow? b. What is the potential at a relative to ground? What is the potential at b relative to ground? c. Where in the circuit ?s the potential the highest? Where is it the lowest? d. Calculate the total power dissipated in both load resistors. e. If the 100 omega resistor is replaced by a short circuit, ?s the total power absorbed by the 40 omega resistor greater than, equal to, or less than the total power initially absorbed by both resistors? f. How much power is delivered by each source (include the effect of the internal resistances)?

Explanation / Answer

a. applying KVL equation,
5i -12 + 40*i +3 +5i + 100i = 0
150i = 9
i = 9/150 = 0.06 A
it flows from a to b.

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b) potential at a = - 5 *0.06 + 12 = 11.7 Volt

potential at b = 11.7 - 40*0.06 - 3 = 6.3 volt

c) potential is lowest at point between 5ohm resistor and 12V .
= - 5 x0.06 = - 0.3 volt relative to ground.
highest. at point a = 11.7 volt

d) Power = i^2R
total power = 0.06^2 (40 +100) = 0.504 watt

e)if 100ohm is shortcircuited then current in circuit wil increase.
power = i^2 * R
so power will also increase.

f) power by source = VI = ( -3 x 0.06) + (12 *0.06) = 0.54 Watt
after including internal resistors :

Power = 0.54 - (0.06^2 * (5+5)) = 0.504 Watt

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