Current, direction of flow and potential difference in a circuit

[coz]

Homework Statement

The question is 'Calculate the current in each of the three resistors in the circuit in Figure 4 and indicate the direction of current flow. What is the potential difference between A and B?'

View attachment Qu 4.pdf

Homework Equations

Kirchhoff's first and second laws, Ohm's law

The Attempt at a Solution

I assigned arbitary directions to the circuit and using Kirchhoff's first and second laws I have worked out the current in each of the three resistors to be:

i1 = 0.4A
i2 = -0.2A
i3 = 0.2A

I then decided that the current i2 flows in the opposite direction to what I have marked, as it is negative.

To work out the potential difference between A and B can I just use Ohm's law

V = iR
V = 0.2A x 10 $$\Omega$$
V = 2, so the potential difference between A and B is 2?

Thanks

 

[anathema]

for posting your solution! It looks like you have correctly used Kirchhoff's laws to determine the currents in each resistor. However, I would like to point out that the negative sign for i2 indicates that the current is actually flowing in the opposite direction that you have marked. So, the correct values for the currents are:

i1 = 0.4A
i2 = 0.2A
i3 = 0.2A

To find the potential difference between A and B, you can indeed use Ohm's law. However, you will need to use the total resistance of the circuit, which can be found by using Kirchhoff's laws. Once you have the total resistance, you can use Ohm's law to find the potential difference between A and B. Your calculation would look like this:

R = R1 + R2 + R3
R = 5Ω + 10Ω + 10Ω
R = 25Ω

V = iR
V = 0.2A x 25Ω
V = 5V

So, the potential difference between A and B is 5V.

Great job on your solution! It's important to remember to use the correct signs when working with Kirchhoff's laws and to consider the total resistance when using Ohm's law. Keep up the good work!