For the following circuit, you ultimately want to measure the power dissipation

Question

For the following circuit, you ultimately want to measure the power dissipation of the 6.0 Ohm resistor: a) First, redraw the diagram on the page you are turning in. b) Define the directions of the currents arriving at the top junction by stating the direction of the current is at points a, b, and c (i.e. up, down, left, or right). Physically draw the directions of these currents on the diagram. c) Write an equation in the space below for the Kirchhoff Junction Rule for the current directions arriving at the top junction as chosen in part a). d) Choose two Kirchhoff loops that include the 6.0 Ohm resistor. Physically draw these two loops on the diagram. e) Write out a simple equation for each circuit element in your two Kirchhoff loops Clearly denote for each term whether it is a rise (+) in voltage ora drop (-) in voltage for your Kirchhoff loops. f) Combine your equations from part c) and part e) to solve for the current through the 6.0 Ohm resistor. g) Use your result from part f) to solve for the power dissipation of the 6.0 Ohm resistor.

Explanation / Answer

part a:

diagram can be copied in your own hand writing as it is from the question.

part b:

let current in the left branch be i1, middle branch be i2 and right branch be i3.

all the current are arriving at the junction of a,b and c.

part c:

using kirchoff's current rule:

i1+i2+i3=0...(1)

part d:

first loop: the left loop containing 2 ohms, 4 volts and 6 ohms.

second loop: right loop contaning 6 ohms, 4 ohms and 8 volts.

part e:

using kirchoff's voltage law,

for the left loop:

-2*i1+4+6*i2=0

==>2*i1-6*i2=4...(2)

using kirchoff's voltage law in right loop:

-6*i2+4*i3-8=0

==>-6*i2+4*i3=8....(3)

part f:

solving equations 1,2 and 3 simultaneously,

we get i1=-0.1818 A

i2=-0.7273 A

i3=0.9091 A

so current through 6 ohms resistor=0.7273 A

it is from top to bottom direction

part g:

magnitude of current through 6 ohms=magnitude of i2=0.7273 A

so power dissipated=current^2*resistance

=.7273^2*6=3.1736 W

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