# Help in solving an electricity circuit problem involving Kirchoff's law

• Eobardrush
In summary: The fact that the diagram shows an arrow coming from E1 as 1.75A makes it look like its the current for E1. But it's not. Its the combination of the current for E1 and the current for E2.
Eobardrush
Homework Statement
Calculate EMF of E1
Relevant Equations
V=IR
E=IR1+IR2
I=I1+I2

My initial solving method was taking 1.75A and adding the resistors at the 1st loop(4 and 8 ohms) to get the answer

V=IR
V=1.75(4+8)
V=21V

But the answer sheet uses 0.75A instead of 1.75A to find EMF of E1.

So according to the answer sheet its
V=0.75(4+8)
V=9V

0.75A is the answer for the i) question. And I am confused as to why use 0.75 instead of 1.75. Isn't 1.75A the current transferred by the E1 battery since its even coming from the direction of E1?

Eobardrush said:
Homework Statement:: Calculate EMF of E1
Relevant Equations:: V=IR
E=IR1+IR2
I=I1+I2

View attachment 295223

My initial solving method was taking 1.75A and adding the resistors at the 1st loop(4 and 8 ohms) to get the answer

V=IR
V=1.75(4+8)
V=21V

But the answer sheet uses 0.75A instead of 1.75A to find EMF of E1.

There might be a couple of missteps you made there.

But let's start from the basics. What is Kirchhoff's first law? (Hint: it doesn't have anything to do with voltage. So the fact that you jumped into using voltage from the get-go is perhaps the main misstep.)

Eobardrush said:
So according to the answer sheet its
V=0.75(4+8)
V=9V

0.75A is the answer for the i) question. And I am confused as to why use 0.75 instead of 1.75. Isn't 1.75A the current transferred by the E1 battery since its even coming from the direction of E1?

The answer sheet is correct. This should be more obvious after you've solved part i.

Delta2
collinsmark said:
There might be a couple of missteps you made there.

But let's start from the basics. What is Kirchhoff's first law? (Hint: it doesn't have anything to do with voltage. So the fact that you jumped into using voltage from the get-go is perhaps the main misstep.)
The answer sheet is correct. This should be more obvious after you've solved part i.

Isn't the first law about currents dividing. Basically I1=I2+I3

But since we are finding the EMF of the battery, shouldn't we use the total current, therefore I1?

In other words shouldn't the current BEFORE it splits be the actual current transferred by the battery E1?
That is the reason why I did not use 0.75 since that is the current after the total current was divided

Eobardrush said:
That is the reason why I did not use 0.75 since that is the current after the total current was divided
If you apply Kirchhoff's voltage law in the upper loop (which you need to do to find the emf E1), which current shows up in the equation?

Delta2
Eobardrush said:
Isn't the first law about currents dividing. Basically I1=I2+I3

But since we are finding the EMF of the battery, shouldn't we use the total current, therefore I1?

In other words shouldn't the current BEFORE it splits be the actual current transferred by the battery E1?
That is the reason why I did not use 0.75 since that is the current after the total current was divided
Kirchhoff's first law states that the sum of currents meeting at a point is zero.

Look at the left part of the figure. There are three arrows present, and two of them are labeled with known currents. Using Kirchhoff's first law, find the current in the third. (And pay attention to the arrows, or at least the directions of the currents, if you want to define your own arrows. The directions of the currents are important in this step, whether that's based on the given arrows or your own arrows.)

Hi @Eobardrush. I'm guessing you are struggling with some of the basics. See if this helps,

The 4Ω and the 8Ω resistors are in series, so I don’t think I’m giving too much away when I say you can replace them by a new single 12Ω resistor.

You can now work through these questions:
a) What current passes through the (new) 12Ω resistor? Explain.
b) Using your answer to part a), what is the voltage across the (new) 12Ω resistor? Explain.

Steve4Physics said:
Hi @Eobardrush. I'm guessing you are struggling with some of the basics. See if this helps,

The 4Ω and the 8Ω resistors are in series, so I don’t think I’m giving too much away when I say you can replace them by a new single 12Ω resistor.

You can now work through these questions:
a) What current passes through the (new) 12Ω resistor? Explain.
b) Using your answer to part a), what is the voltage across the (new) 12Ω resistor? Explain.
Actually I do understand question A and B here. But I am struggling to understand why there is a 1.75A in the diagram. Is that maybe the combined current for E2 and E1? If so then I think I understand.

The reason I was struggling is that I am not 100% sure if 1.75A is just the current for E1 or the combination of both E1 and E2

The fact that the diagram shows an arrow coming from E1 as 1.75A makes it look like its the actual total current from E1 so its making it a bit confusing

And sorry I know I am really dumb. Been self teaching myself actually

Last edited:
Eobardrush said:
Actually I do understand question A and B here.
You have not given answers, so there is no way of telling if you have a correct understanding or not.

Eobardrush said:
But I am struggling to understand why there is a 1.75A
The cell is ideal (a fixed emf and zero internal resistance). That means the cell can deliver any current (e.g. 0.000001A or 1000000A) depending on what’s in the rest of the circuit. As a consequence, knowing the current through the cell (1.75A) does not directly help you to find the cell’s emf.

I suggest you read the next paragraph carefully and then go back to the Post #6 questions.

An ideal cell’s emf is always equal to the voltage between the its terminals. Using this fact, and the answers to Post #6 questions a) and b) let's you find E1.

Delta2

## 1. What is Kirchoff's law and how does it apply to electricity circuits?

Kirchoff's law, also known as Kirchoff's circuit laws, are a set of rules used to analyze and solve problems in electrical circuits. These laws are based on the principles of conservation of charge and energy. Kirchoff's current law states that the sum of currents entering a junction in a circuit must equal the sum of currents leaving the junction. Kirchoff's voltage law states that the sum of voltage drops in a closed loop must equal the sum of voltage rises.

## 2. How do I apply Kirchoff's law to solve an electricity circuit problem?

To apply Kirchoff's law, you will need to identify all the branches and junctions in the circuit. Then, you will need to write equations for the currents and voltages in each branch, using Kirchoff's current and voltage laws. Finally, you can solve the resulting system of equations to find the values of the current and voltage in each part of the circuit.

## 3. What are the common mistakes to avoid when using Kirchoff's law to solve an electricity circuit problem?

One common mistake is not properly labeling the currents and voltages in the circuit. It is important to assign a direction to each current and a polarity to each voltage, and to be consistent with these assignments throughout the problem. Another mistake is not properly setting up the equations using Kirchoff's laws. Make sure to include all the necessary terms and to use the correct signs for the voltage drops and rises.

## 4. Can Kirchoff's law be used for any type of circuit?

Yes, Kirchoff's law can be applied to any type of circuit, including series circuits, parallel circuits, and more complex circuits. However, for more complex circuits, it may be necessary to use additional techniques, such as mesh analysis or nodal analysis, in addition to Kirchoff's laws.

## 5. Are there any real-world applications of Kirchoff's law?

Yes, Kirchoff's law is widely used in the design and analysis of electrical circuits in various industries, such as electronics, power systems, and telecommunications. It is also used in the development of renewable energy sources, such as solar panels and wind turbines. Additionally, Kirchoff's law is used in the design of electronic devices, such as computers and smartphones, to ensure proper functioning of the circuits.

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