P 5.3-6 Use superposition to find the value of the current i in Figure P 5.3-6.

Figure P 5.3-6

Total current i is found by considering i due to each power source separately and then adding them up, so

First find I due to just the 15 V source, so deactivate the 15 mA and the 30 mA sources and our circuit becomes:

To find i let’s use mesh currents, so our circuit with mesh currents looks like

First mesh

Second mesh

Now solve for i₁ and i₂

Multiply mesh eq 1 by 3 and mesh eq 2 by 2 and we have

Now add the two equations

Solve for i₁

From second mesh equation

so

Ok, Now the 15 mA circuit, deactivate the 15 V and the 30 mA sources and we have

Again set up mesh currents

This time

Write up mesh equations

Simplify some

This time multiply top equation by 3 and bottom by 2

Now add

Solve for i2

Use second equation and

so

Ok, Now the 30 mA circuit, deactivate the 15 V and the 15 mA sources and we have

Again set up mesh currents

Write up mesh equations, we have a super mesh this time

And

The normal mesh equation

In equation 2 replace with the result of the first super mesh equation

And the other eq

Multiply the first equation by 3 and the second by 2

Now add them

We can find from

So

Now add the three parts together

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This page last updated on February 23, 2019