Calculating Internal Resistance and Maximizing Power Transfer in a 24V Supply

[licklecee]

Homework Statement

A 24 voltt supply has a terminal voltage of 20 volts when connected to a 40R Load Resistor.

Calculate the internal resistance of the supply

State the conditions under which maximum power will be transferred to load.

Homework Equations

V = E - Ir

V = p.d. across resistor R
E = e.m.f. of the cell
I = current
r = internal resistance of the cell

The Attempt at a Solution

V = E - Ir

I = V/r
I = 24/20
I = 1.2 amps

V = 24 - ( 1.2 x 24 )

V = 4.8


Hi guys i was wondering if you could shed some light on this problem. I think i am right but i was stumped quite early and i have no electronics background. any assistance would be terrific. Also was wondering if there is a 24 volt supply and a terminal voltage of 24 volts after being conneted to 40R load resistor, does this mean the internal resistance is 4volts or 20 volts ?

Thanks

 

[Vagrant]

I = current
r = internal resistance of the cell
I = V/r
I = 24/20

No. I is not equal to V/r
To calculate the current, you need to take into account both R and r.
Also, what are the values of V and E from the problem statement?

 

[licklecee]

Okay thank you, well they haven't actually provided the value of V and E. The known values are :

24 Volt Supply with a terminal voltage of 20 volts when connected to a 40R load resistor.

That is all the information that was provided, Also it says 40R, what does R refer to ?

Thank you very much !

 

[Redbelly98]

It means the resistor is 40 ohms. Writing it as "40R" is the jargon of professional electrical engineers ... there actually are good reasons for this, but the reasons don't apply in introductory courses.

Question for you: what is the voltage across the 40 ohm resistor?

p.s. welcome to Physics Forums.

 

[licklecee]

Thank you :),

Oh right so it's another way of saying ohms. Lovely,

It would be 20 volts i believe since the terminal voltage is 20 volts so that should be the voltage passing through the resistor.

Would the E.M.F. be referring to the voltage after the internal resistance has been taken into account ?

 

[Vagrant]

Would the E.M.F. be referring to the voltage after the internal resistance has been taken into account ?

No, terminal voltage is the the voltage across the terminals of the battery after internal resistance has been taken into account.

Here are some links where you can read up a little about it.
http://www.coolschool.ca/lor/PH12/unit6/U06L04.htm"
http://www.iop.org/activity/education/Teaching_Resources/Teaching%20Advanced%20Physics/Electricity/EMF%20and%20Internal%20Resistance/page_3610.html"

 

[Redbelly98]

Thank you :),

Oh right so it's another way of saying ohms. Lovely,

It would be 20 volts i believe since the terminal voltage is 20 volts so that should be the voltage passing through the resistor.

Yes.

Would the E.M.F. be referring to the voltage after the internal resistance has been taken into account ?

EMF is the voltage when no current is flowing, i.e. the 24V in this case. (Not sure if that's what you meant.)