Solve Kirchhoff's Laws Homework: Find Current I in a Circuit

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In summary: This voltage is called the "current through the resistor." Kirchhoff's law tells us that the current through the resistor is equal to the sum of the voltages across the resistor. In this circuit, the voltage across the 10 ohm resistor in the first loop is 5 volts, the voltage across the 10 ohm resistor in the bottom loop is 10 volts, and the voltage across the junction is 15 volts. Therefore, the current through the 10 ohm resistor in the first loop is 5 + 10 + 15 = 30 volts, and the current through the 10 ohm resistor in the bottom loop is 10 - 10 - 15 = 0 volts.
  • #1
Barnt
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Homework Statement


Use Kirchhoff's Law to find the current I in the circuit shown below. Choosing the best loop can simplify the problem. (a) Which loop in the circuit should you choose? (b) Calculate the current I

upload_2018-9-10_14-11-31.png


Homework Equations



Kirchhoff's Second Law
∑V = 0

and the junction law
∑I = 0

The Attempt at a Solution


Firstly, the mark scheme says that the third loop should be used. The reason being that loop is the only loop with the current I going through the resistor. It makes sense to use the loop with I being the only current through the resistor. However, I do not understand how they know that the current through the 10 ohm resistor in the first loop is the same as the current through the 10 ohm resistor in the bottom loop.

Secondly, the mark scheme says I = 1.0 A. I'm assuming that was calculated the following way...

0 = 5 + 5 +10I
I = 1 A.

But that does not make sense to me either. I am using the following rule...

upload_2018-9-10_14-22-34.png


When I use that on the bottom loop I get the following -

0 = 5 - 5 - 10I

What am I doing wrong?

Thanks
 

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  • #2
Barnt said:
the mark scheme says that the third loop should be used.
Not sure what is meant by that. There are six loops (pick any two horizontal connections from four). The best choice I see is the top and third horizontal.
Barnt said:
I do not understand how they know that the current through the 10 ohm resistor in the first loop is the same as the current through the 10 ohm resistor in the bottom loop.
It isn't, but we don't care about the current through the bottom resistor.
 
  • #3
Its a bit hard to read your image but..

"neither does current go through BG"

.. is wrong. There is current flowing in BG but you don't need to calculate it.

haruspex said:
There are six loops (pick any two horizontal connections from four). The best choice I see is the top and third horizontal

+1

Remember that a voltage source connected between two nodes forces a known voltage to appear between those nodes.
 

Related to Solve Kirchhoff's Laws Homework: Find Current I in a Circuit

1. What are Kirchhoff's Laws?

Kirchhoff's Laws are fundamental principles in circuit analysis that describe the behavior of electric circuits. They are Kirchhoff's Current Law (KCL), which states that the sum of currents entering a node in a circuit must equal the sum of currents leaving the node, and Kirchhoff's Voltage Law (KVL), which states that the sum of voltage drops around a closed loop in a circuit must equal the sum of voltage sources.

2. How do I apply Kirchhoff's Laws to a circuit?

To apply Kirchhoff's Laws to a circuit, you must first identify all the nodes and loops in the circuit. Then, using KCL and KVL, you can write equations for each node and loop. By solving these equations simultaneously, you can find the values of currents and voltages in the circuit.

3. What is the difference between KCL and KVL?

KCL deals with currents and nodes in a circuit, while KVL deals with voltage drops and closed loops. Both are essential for solving circuit problems and can be used together to determine the values of currents and voltages in a circuit.

4. How do I find the current (I) in a circuit using Kirchhoff's Laws?

To find the current (I) in a circuit using Kirchhoff's Laws, you first need to label all the currents and voltages in the circuit. Then, write equations for each node and loop using KCL and KVL. By solving these equations simultaneously, you can determine the value of the desired current (I).

5. Can Kirchhoff's Laws be used in all types of circuits?

Yes, Kirchhoff's Laws can be applied to all types of circuits, including series, parallel, and combination circuits. These laws are fundamental principles in circuit analysis and are essential for solving complex circuit problems.

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