Find the resistance of the resistor

Thread Starter


Joined Aug 26, 2011
On a real voltage source of \(10V\) with internal resistance of \(100\Omega\), a resistor is connected. The power on the resistor is \(200mW\). Find the resistance.

I know Ohm's law, Kirchhoff's laws, Power formulas

I tried finding R or I from \(R=\frac{P}{I^{2}}\)

This may be an easy example but I don't know I can't find R.
I'm solving harder problems, but can't find this one.
Thanks in advance.


Joined Mar 6, 2009
The source terminal voltage


The load power



and so on to solve for I from a quadratic equation & finally R=P/I^2=0.2/I^2

There is an unexpected outcome by the way......
Last edited:

Thread Starter


Joined Aug 26, 2011
yeah, I tried this
but from the quadratic equation there are two outcomes
I1 and I2,
0.028 and 0.072
Im really confused.

Thread Starter


Joined Aug 26, 2011
wow how can that be true.
never thought there can be two solutions...
I solved problems like this one before, but from the quadratic equation there was only one outcome.
for example I remember this one...

this equation has only one solution, which is 2.

anyway thanks Jony and t_n_k


Joined Dec 26, 2010
It is not difficult to see that there must be two solutions to this problem. The maximum power will be transferred into the load when it is made equal to the generator resistance, in this case 100Ω. This results from the Maximum Power Transfer Theorem:

The load voltage at maximum power will therefore be half the open-circuit value, i.e. 5V, so that the current will be 5V/100Ω = 50mA, and the output power will be 5V*50mA = 250mW.

The load power will also reduce if its resistance is varied either up or down from 100Ω, so we can expect to obtain 200mW for two current levels, one somewhat greater than 50mA and another somewhat less.