# Find the resistance of the resistor

#### Agonche

Joined Aug 26, 2011
30
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
$$P=I^{2}R$$
$$P=\frac{E^{2}}{R}$$
$$P=EI$$

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.

#### t_n_k

Joined Mar 6, 2009
5,455
The source terminal voltage

V=10-100*I

P=0.2=V*I

V=0.2/I=10-100*I

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:

#### Agonche

Joined Aug 26, 2011
30
yeah, I tried this
but from the quadratic equation there are two outcomes
I1 and I2,
0.028 and 0.072
Im really confused.

#### Jony130

Joined Feb 17, 2009
5,227
Simply you have two proper solution to your problem.

#### Agonche

Joined Aug 26, 2011
30
@Jony130
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...

$$6I^{2}-24I-24=0$$
this equation has only one solution, which is 2.

anyway thanks Jony and t_n_k

Joined Dec 26, 2010
2,148
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:

http://en.wikipedia.org/wiki/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.

#### t_n_k

Joined Mar 6, 2009
5,455
Plotting V-I characteristic against the P=0.2W curve shows there are two valid conditions for 0.2W load power.

#### Attachments

• 13.3 KB Views: 21

#### The Electrician

Joined Oct 9, 2007
2,825
$$6I^{2}-24I-24=0$$
this equation has only one solution, which is 2.

anyway thanks Jony and t_n_k
Just as an aside, this equation has two solutions, neither of which is 2.

$$6I^{2}-24I+24=0$$