[College Physics] need help deriving an equation using algebra.
this is a problem for a physics lab but the underlying issue I'm having is just algebra (I think)
The capacitance (C) can now be calculated as C = τ/R. However, since the internal resistance of the source rint is unknown, the experiment must be repeated using a second external resistance value. Comparison of the time constant values between the two measurements will allow the determination of both the capacitance and source resistance values. By equating the capacitance and solving for rint:
[; r_{int} = \frac{\tau_2 R_{ext1} - \tau_1 R_{ext2}}{\tau_1 - \tau_2} ;]
The total resistance is Rext + rint, which you can use in C = τ/R to find the capacitance.
the question at the end of the lab is to derive this equation.
so I first start out by equating both capacitance
[; C_1 = C_2 ;]
capacitance can be re-written using tau and resistance
[; \frac{\tau_1}{R_1} = \frac{\tau_2}{R_2} ;]
but we only have the external resistance of each resistor, so we need to include the internal resistance
[; \frac{\tau_1}{R_{ext1} + r_{int}} = \frac{\tau_2}{R_{ext2} + r_{int}} ;]
..and this is as far as I've gotten. I don't even know if I'm going down the right path here. how would I go about isolating r_int to form the given equation?
thank you!
Posted Mar 26, 2018, 1:07 AM UTC · edited
Are we in the same physics class? I'm finishing up a lab exactly like this as we speak.
Anyway, you're doing great so far. Just multiply both sides by the denominators to get:
[;{ \tau }_{ 1 }R_{ ext2 }+{ \tau }_{ 1 }r_{ int }={ \tau }_{ 2 }R_{ ext1 }+{ \tau }_{ 2 }r_{ int };]Get all the internal resistance variables one one side, and the other variables on the other:
[;{ \tau }_{ 1 }r_{ int }-{ \tau }_{ 2 }r_{ int }={ \tau }_{ 2 }R_{ ext1 }-{ \tau }_{ 1 }R_{ ext2 };]Factor out the internal resistance variable and divide by the difference in time constants:
[;r_{ int }=\frac { { \tau }_{ 2 }R_{ ext1 }-{ \tau }_{ 1 }R_{ ext2 } }{ { \tau }_{ 1 }-{ \tau }_{ 2 } } ;]Edit: If we are in the same class, you probably already know who I am.
wow, that was such a simple step I was overlooking. thanks a lot.
that would be a huge coincidence if we are in the same class. my professor is kinoshita. does that ring a bell? lol.
Yupp, she gave us the data for that lab because my group couldn't get our setup to work.
yeah that lab was an absolute train wreck. my group actually had a working setup but then she turned around and said "nevermind, don't use that data." so essentially our time in lab period was a waste.
I very rarely turn to reddit for homework help, but I was a bit desperate in this situation. I finished the lab last monday except for the error analysis and questions and decided to finish it up tonight. I got stuck (on a simple algebraic issue, which is no surprise) and e-mailed her but received no response. I didn't want to sacrifice easy points by leaving it blank.
I actually have no clue who this is.
Glasses and grey jacket. Sits close to the door, in the front. And frankly the whole class has been a bit of a train wreck. We're still about 2 weeks behind schedule.