Using Kirchhof's laws to solve a circuit

[Asmaa Mohammad]

Homework Statement

In the circuit shown in the figure (attached with the solution). Determine:
1. the reading of the ammeter when the key (K) is open.
2. The reading of the ammeter when the key (K) is closed.

Homework Equations

The Attempt at a Solution

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What confuses me in the circuit above is that when the key is open, I will have only one loop to work on, and that will make only one equation (equation no.2) and then I will have two unknown values, and I will not be able to find i₂ (the current passing through the ammeter), so what should I do here?

 

[gneill]

What confuses me in the circuit above is that when the key is open, I will have only one loop to work on, and that will make only one equation (equation no.2) and then I will have two unknown values, and I will not be able to find i₂ (the current passing through the ammeter), so what should I do here?

How many independent currents can you have if there is a single loop?

 

[Asmaa Mohammad]

How many independent currents can you have if there is a single loop?

When I have only loop 1, I will have two currents: i₁ and i₂.

 

[cnh1995]

When I have only loop 1, I will have two currents: i₁ and i₂.

Are they two different currents?

 

[Asmaa Mohammad]

Are they two different currents?

Oh, they aren't.
So there will be only one current, and the equation will go like this:
20-5 = 15i -----> i = 1 A
So in the first case the ammeter reads 1 A.

 

[cnh1995]

Oh, they aren't.
So there will be only one current, and the equation will go like this:
20-5 = 15i -----> i = 1 A
So in the first case the ammeter reads 1 A.

Right.
What about the second case?

 

[Asmaa Mohammad]

Right.
What about the second case?

OK, I will solve the three equation I had after applying Kirchhoff's laws.
The value of i2 is 2.57 A.

 

[cnh1995]

Sorry for relpying so late! I was travelling.

Your first equation is incorrect seeing the directions of the currents.

For second case, you have two independent loops. So use two loop currents.

See this example.

 

[Asmaa Mohammad]

Your first equation is incorrect seeing the directions of the currents.

Oh, yes, I can't believe I still do these silly mistakes with Kirchhoff's laws until now.
Anyway, it will be like this:
i₁ = i₂ + i₃ ----> 1
15 = 10 i₂ + 5i₁ -----> 2
15 = 5i₁ + 5 i₃ -----> 3

Ok, and I will use two loop currents. It will be like this:
15 = 10i₂ + 5i₁ ------> 2
15 = − 5i₂ + 10 i₁ -----> 4

Then i₂ = 0.6 A

 

[cnh1995]

Then i₂ = 0.6 A

I am getting the same answer.

 

[Asmaa Mohammad]

I am getting the same answer.

Thank you, thank you, thank you!

 

[cnh1995]

Thank you, thank you, thank you!

No probs!