How to Rearrange the Formula to Find Load Resistance?

[Kobayashi]

[SOLVED] Calculate Load Resistance

Homework Statement

Find RL if PL is 90W.

Homework Equations

PL= ((V^2)*(RL))/((RL+r)^2)

The Attempt at a Solution

I calculated the internal resistance to be 5 Ohms on my circuit with a supply voltage of 100V

So, 90W = ((100^2) * (RL))/((RL + 5)^2)

From this equation how do I rearrage the formula to get the Load Resistance?

 

[marcusl]

Expand the square in the denominator, cross multiply it to the left side. Collect the linear terms (linear in RL) onto the left side, so the right is zero. This is now a standard quadratic equation, apply the quadratic formula to solve.

 

[Kobayashi]

So,

R^2 + 2Rr + r^2 + 90 - (V^2*R)

Becomes,

R^2 + 10R + 115 - 10000R =0

R^2 + 9990R + 115 = 0

From this I still can't get the correct answer when using the quadratic formula. Is it the load voltage or the supply voltage you use in this case? The two answers should be 100.75 Ohms and 0.25 Ohms. Any idea where I'm going wrong?

 

[hage567]

You are messing up the algebra.

Starting with your first equation:

$$P_L= \frac{V^2R_L}{(R_L+r)^2}$$

You need to multiply through by the denominator so you get

$$P_L(R_L+r)^2 = V^2R_L$$

Now expand the bracket, and then multiply through by $$P_L$$. Group like terms and then use the quadratic formula.

Use the supply voltage.

 

[Kobayashi]

Thanks, I now managed to get the correct answer.