Solving circuits with superposition (2 problems)

[Rellek]

Homework Statement

Screenshots have everything.

Homework Equations

$V = iR$
Voltage/current division
Mesh analysis
Adding resistors in parallel/series
Kirchhoff's Laws

The Attempt at a Solution

First problem

I started with turning off the current source. You are left with a simple series circuit with a dependent source because the part with the current source becomes an open circuit. I used Kirchhoff's voltage rule around the loop and got: $$-12 + i_{1} + 3i_{1} + 2i_{1} = 0$$

Which yields $i_{1} = 2$

I then turned off the voltage source and activated the current source. I chose to use mesh analysis because it seemed to be the quickest way. The current you are left with is a resistor and a dependent source, another resistor, and your current source in parallel. The mesh current on the left is $i_{x}$ and on the right is $i_{y}$. Using KVL for the supermesh around the perimeter: $$i_{x} +3i_{y}+2i_{x} = 0$$
and also
$$i_{y} - i_{x} = 6$$

Which solves $i_{x}$ as -3 amperes. So, adding the first current and the second current gives -1 Amperes?

Second question

Again, I turned off the current source first. This leaves you with 2 resistors in series (parallel with the V source) and another 30 Ohm resistor in parallel. Since they all shared one node, the voltage should stay the same, right?

If that's true, you can use Ohm's law to find the current over the strand on the right will be $$\frac {200}{100} = 2$$

This next part is where I have a bit of a trouble. Turn off voltage source, turn on current source. If you look at the second picture, and replace the voltage source with a short circuit, does this mean that the 30 Ohm resistor can be ignored, because the current will always go through the short circuit instead of the path with the resistor?

If this is true, you can just use current division, like so $$3 \frac {60}{40+60} = 1.8$$

And you know this will be in the opposite direction from the previous current value, so $2 - 1.8 = .2$ so the current $I_{0}$ will be .2 Amperes. Is this correct? Thanks!

 

[Rellek]

No one?

 

[SammyS]

Homework Statement

Screenshots have everything.

Homework Equations

$V = iR$
Voltage/current division
Mesh analysis
Adding resistors in parallel/series
Kirchhoff's Laws

The Attempt at a Solution

First problem

I started with turning off the current source. You are left with a simple series circuit with a dependent source because the part with the current source becomes an open circuit. I used Kirchhoff's voltage rule around the loop and got: $$-12 + i_{1} + 3i_{1} + 2i_{1} = 0$$

Which yields $i_{1} = 2$

...

Thanks!

(It's too soon to be bumping your own thread ! Please review the Forum Rules.)

You should get $-12 + i_{1} + 3i_{1} + v_{2i_{1}} = 0\ .$

But you would also need $\ i_1 = -2i_1 \$ by KCL.(It's easy enough to check your answer to this one by using Kirchhoff's Current Law directly.)

 

[SammyS]

Homework Statement

Screenshots have everything.
...

The Attempt at a Solution

Second question

Again, I turned off the current source first. This leaves you with 2 resistors in series (parallel with the V source) and another 30 Ohm resistor in parallel. Since they all shared one node, the voltage should stay the same, right?

If that's true, you can use Ohm's law to find the current over the strand on the right will be $$\frac {200}{100} = 2$$

This next part is where I have a bit of a trouble. Turn off voltage source, turn on current source. If you look at the second picture, and replace the voltage source with a short circuit, does this mean that the 30 Ohm resistor can be ignored, because the current will always go through the short circuit instead of the path with the resistor?

If this is true, you can just use current division, like so $$3 \frac {60}{40+60} = 1.8$$

And you know this will be in the opposite direction from the previous current value, so $2 - 1.8 = .2$ so the current $I_{0}$ will be .2 Amperes. Is this correct? Thanks!

The second one looks good.

 

[HalfLostAndSearching]

Your approach to solving the first problem using superposition is correct. By turning off the current source, you can focus on the dependent source and solve for the current through it using KVL. Similarly, by turning off the voltage source, you can use mesh analysis to solve for the current through the dependent source in the other direction. Adding these two currents together gives you the total current through the dependent source, which can then be used to calculate the current through the rest of the circuit. Your final answer of -1 Amperes is correct.

For the second problem, your approach is also correct. By turning off the current source, you can focus on the parallel resistors and use Ohm's law to calculate the current through the right strand. When you turn off the voltage source and turn on the current source, the 30 Ohm resistor can be ignored since all the current will flow through the short circuit. Your use of current division to calculate the current through the rest of the circuit is also correct. Your final answer of 0.2 Amperes for the current $I_{0}$ is correct. Good job!