# What are the currents at each resistor?

• chuvacjoe
In summary: OK. We now have definite directions for the currents: I1 to the right, I3 to the right, and I2 to the left.
chuvacjoe
1. The problem statement, all variables
and given/known data

I3 + I1= I2

## The Attempt at a Solution

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Hello and welcome to PF!

It is very important to specify the directions that you are assuming for each of the three currents. Otherwise, there is no way for us to check the signs in your equations.

For each equation you should state whether it comes from a junction rule or from a loop rule; and, tell us which junction/loop corresponds to each equation.

Equation #1- Kirchoff's junction current rule
Equation #2- Upper Loop clockwise from 20V source
Equations #3- Lower Loop rule counterclockwise

Please specify the direction you are choosing for ##I_1##, the direction you are choosing for ##I_2##, and the direction you are choosing for ##I_3##. This is essential for getting the correct signs in the equations.

That's probably where my mistake is at, but I3 counterclockwise, I 2 counterclockwise, and I 1 counterclockwise? This is the part I'm a little confused about because I've been learning kirchhoffs rules from a book and khan's academy. They all flow to the closest stronger volt source?

It would be clearer if you specified ##I_1## as to the right or to the left through the 30Ω resistor. Similarly for the other two currents. On your circuit diagram, these directions should be indicated with arrows.

I 1 to the right, I 3 to the right, and i 2 to the left as assumed from my first equation I 1 +I 3=i 2

chuvacjoe said:
I 1 to the right, I 3 to the right, and i 2 to the left as assumed from my first equation I 1 +I 3=i 2
Note that the equation I1 + I3 = I2 would have also resulted from taking I1 to the left, I3 to the left and I2 to the right.

But, OK. We now have definite directions for the currents: I1 to the right, I3 to the right, and I2 to the left.

Your junction equation I1 + I3 = I2 is correct.

Let's look at your loop equation for the top loop. You wrote

20 - 30I1 + 5I2 - 10 = 0.

There is a sign error in this equation. Can you explain why you chose each of the four signs on the left?
Why +20? Why - 30I1? Why +5I2? Why -10?

It is important to note that you generally will not know ahead of time the correct directions for the currents. That is part of what you will determine when solving the problem. But, the nice thing is that you can assume any direction you want for any of the currents. If your initial choice of direction for a current turns out to be wrong, then you will get a negative answer for that current. The negative sign indicates that the current is actually in the opposite direction from what you initially assumed.

So, for example, if you end up getting I2 = -4 A, then the current I2 will be 4 A in a direction opposite of what you initially chose when setting up your equations.

But it is essential to make an initial choice for the direction of each current and stick with that choice while setting up the signs in your equations.

## What are the currents at each resistor?

The currents at each resistor can be calculated using Ohm's Law, which states that the current (I) is equal to the voltage (V) divided by the resistance (R). So, the formula for calculating current at a resistor is I = V/R.

## How do I measure the currents at each resistor?

To measure the currents at each resistor, you will need a multimeter. Set the multimeter to the current (Amps) setting and connect the probes to the resistor in series. The multimeter will display the current flowing through the resistor.

## What factors affect the currents at each resistor?

The currents at each resistor can be affected by the resistance of the resistor itself, the voltage applied across the circuit, and the presence of any other components in the circuit such as capacitors or inductors.

## What happens if there is no current at a resistor?

If there is no current at a resistor, it means that there is no voltage drop across that resistor. This could be due to a break in the circuit or if the resistor has a very high resistance value. In this case, no current will flow through the resistor.

## What is the difference between series and parallel currents at resistors?

In a series circuit, the current at each resistor is the same, as it is only one path for the current to flow. In a parallel circuit, the current is divided among the resistors based on their individual resistance values. This means that the current at each resistor will be different in a parallel circuit.

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