Kirchoff's law and circuit analysis

Can you check this?In summary, when solving for the three currents using symbols, it is discovered that the current flowing through the unknown resistor is not consistent with any of the given choices. There is something wrong with the given numbers and it is not possible to determine the correct answer.
  • #1
fight_club_alum
63
1
Homework Statement
23. In the figure, if I = 80 mA, determine the resistance R
Relevant Equations
Kirchoff's law
241786

I assumed the current flows from the 20V so,
20V - 100 (i1) - Ri2 = 0
First loop
20V = 100i1 + Ri2

Second loop
+Ri2 + 40V - 200(0.08) = 0
Ri2 = -24

Back to equation 1

20 v = 100i1 + (-24)
therefore, i 1 = 0.44

For loop two:
i1 - i2 = i3
0.44 - i2 = 0.08
therefore i2 = 0.36 ohms

So, if R i2 = -24

R (0.36) = -24

R = -66.6666667 ohms
This is none of the choices and the answer key says d

Someone please help
 
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  • #2
There is something wrong with the given numbers. I agree with your solution.

On edit: Actually this problem is a bit tricky. Try this: ignore the given 80 mA current and solve for the three currents as if they were unknown using symbols, e.g. ##E_1## for the 20 V battery, ##2E_1## for the 40 V battery, ##R_1## and ##2R_1## for the known resistors and ##R## for the unknown resistor. You will discover something peculiar about the current that flows through ##R##. However, in view of this result, I don't see how one can get any of the listed choices.
 
Last edited:

Related to Kirchoff's law and circuit analysis

1. What is Kirchoff's law?

Kirchoff's law, also known as Kirchoff's circuit laws, are two basic principles that govern the behavior of electric circuits. These laws were developed by German physicist Gustav Kirchoff in the mid-19th century and are widely used in circuit analysis and design.

2. What are the two laws in Kirchoff's circuit laws?

The two laws in Kirchoff's circuit laws are the Kirchoff's current law (KCL) and the Kirchoff's voltage law (KVL). KCL states that the sum of all currents entering a node in a circuit must equal the sum of all currents leaving the node. KVL states that the sum of all voltage drops in a closed loop in a circuit must be equal to the sum of all voltage rises.

3. How are Kirchoff's laws used in circuit analysis?

Kirchoff's laws are used in circuit analysis to determine the values of currents and voltages in a circuit. By applying KCL and KVL to different parts of a circuit, one can solve for the unknown values and understand the behavior of the circuit.

4. Are there any limitations to Kirchoff's laws?

Yes, there are limitations to Kirchoff's laws. These laws assume ideal conditions, such as point-like connections and perfectly conducting wires, which may not be the case in real-world circuits. Additionally, these laws do not take into account the effects of electromagnetic interference and non-linear elements in a circuit.

5. Can Kirchoff's laws be applied to all types of circuits?

Yes, Kirchoff's laws can be applied to all types of circuits, including DC and AC circuits, as long as the circuit is in a steady-state condition. In cases of transient conditions, where the circuit is changing over time, additional equations and laws may need to be incorporated in the analysis.

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