Electric Circuit using Kirchoff's rules

In summary, the given resistors have values of R1 = 15.0 Ω, R2 = 10.0 Ω, and R3 = 8.00 Ω. Using Kirchoff's rules and applying KVL/KCL, the currents through R1, R2, and R3 are found to be I1 = 1.114A, I2 = 0.143A, and I3 = 1.257A respectively. The direction of the current for each resistor can be determined by referring to the marked up circuit diagram.
  • #1
Jakarto
11
0

Homework Statement


We are given that R1 = 15.0 Ω, R2 = 10.0 Ω, and R3 = 8.00 Ω. What is the current and direction of the current through each resistor? Again, I have no idea how to do this, I got my answer from chegg, but I don't know if this is correct.

4.PNG

Homework Equations



V = IR[/B]

The Attempt at a Solution



Using Kirchoff's rules , for the loop ADCBA, starting from D, we have:
(-10ohm * i1) + (10V) - 15ohm(i1+i2) +(20V) = 0[/B]
(25ohm * i1) + (15ohm * i2) = 30V
(5 * i1) +(3 * i2) = 6 to the -(i) direction ?

Now, applying Kirchoff to DCFED, starting from D:
(-10ohm * i1) + (10V) + (8ohm * i2) = 0
(10ohm * i1) - (8ohm * i2) = 10V
(5 * i1) - (4 * i2) = 5V to the -(ii) direction ?
After solving, we get:
i1 = 1.14A for R2?
i2 = 0.142A for R3?
i3 = 1.256A for R1?

Are the currents and directions correct? If not, can you tell me what the direction is at least?
 
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  • #2
Have you tried reading your textbook or a textbook? This question should be one of the first things mentioned.
 
  • #3
Your equations look correct but after solving I get very slightly different answers...

I1 = 1.114A
I2 = 0.143A
I3 = 1.257A

However...

Jakarto said:
Are the currents and directions correct? If not, can you tell me what the direction is at least?

Before you apply KVL/KCL it's essential to mark up the circuit with the currents I1 and I2 including arrows to define what you mean by +ve current flow. Then, after applying KVL/KCL and solving, if I1 or I2 turns out to be +ve or -ve you know which direction that is by referring to your drawing.

Note: You need BOTH the drawing and the calculated currents for a valid answer. That's because the direction you choose for +ve current is arbitrary. Your classmates may have chosen to define a different direction as +ve, in which case they would have got -ve answers for the currents. That would be an equally valid answer. The only time it's not an arbitrary choice is when the problem statement tells you to make a particular choice.
 
  • Like
Likes Jakarto
  • #4
Okay, thanks again CWaters!
 

1. What are Kirchoff's rules and how are they used in electric circuits?

Kirchoff's rules, also known as Kirchoff's laws, are a set of fundamental principles used to analyze and solve electric circuits. They are based on the conservation of charge and energy, and are used to determine the voltage, current, and resistance values in a circuit.

2. How do Kirchoff's rules apply to series and parallel circuits?

In a series circuit, Kirchoff's voltage law states that the total voltage in a closed loop must equal the sum of the individual voltage drops. In a parallel circuit, Kirchoff's current law states that the total current entering a junction must equal the sum of the currents leaving the junction.

3. What is the difference between Kirchoff's voltage law and Kirchoff's current law?

Kirchoff's voltage law, also known as the loop rule, states that the algebraic sum of the voltages around a closed loop in a circuit must equal zero. Kirchoff's current law, also known as the junction rule, states that the algebraic sum of the currents entering and leaving a junction in a circuit must equal zero.

4. How do you apply Kirchoff's rules to solve a circuit with multiple loops?

To solve a circuit with multiple loops using Kirchoff's rules, you must first label the currents and voltages in the circuit. Then, you can use Kirchoff's voltage law and Kirchoff's current law to create a system of equations, which can be solved to find the values of the unknown variables.

5. Can Kirchoff's rules be applied to circuits with non-ideal components?

Yes, Kirchoff's rules can be applied to circuits with non-ideal components, such as resistors with varying resistances or capacitors with leakage currents. However, the calculations may become more complex and may require the use of additional equations or techniques.

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