Find the currents flowing in the circuit in
[link] .
Strategy
This circuit is sufficiently complex that the currents cannot be found using Ohm’s law and the series-parallel techniques—it is necessary to use Kirchhoff’s rules. Currents have been labeled
,
, and
in the figure and assumptions have been made about their directions. Locations on the diagram have been labeled with letters a through h. In the solution we will apply the junction and loop rules, seeking three independent equations to allow us to solve for the three unknown currents.
Solution
We begin by applying Kirchhoff’s first or junction rule at point a. This gives
since
flows into the junction, while
and
flow out. Applying the junction rule at e produces exactly the same equation, so that no new information is obtained. This is a single equation with three unknowns—three independent equations are needed, and so the loop rule must be applied.
Now we consider the loop abcdea. Going from a to b, we traverse
in the same (assumed) direction of the current
, and so the change in potential is
. Then going from b to c, we go from
to +, so that the change in potential is
. Traversing the internal resistance
from c to d gives
. Completing the loop by going from d to a again traverses a resistor in the same direction as its current, giving a change in potential of
.
The loop rule states that the changes in potential sum to zero. Thus,
Substituting values from the circuit diagram for the resistances and emf, and canceling the ampere unit gives
Now applying the loop rule to aefgha (we could have chosen abcdefgha as well) similarly gives
Note that the signs are reversed compared with the other loop, because elements are traversed in the opposite direction. With values entered, this becomes
These three equations are sufficient to solve for the three unknown currents. First, solve the second equation for
:
Now solve the third equation for
:
Substituting these two new equations into the first one allows us to find a value for
:
Combining terms gives
Substituting this value for
back into the fourth equation gives
The minus sign means
flows in the direction opposite to that assumed in
[link] .
Finally, substituting the value for
into the fifth equation gives
Discussion
Just as a check, we note that indeed
. The results could also have been checked by entering all of the values into the equation for the abcdefgha loop.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.