Since R depends on which then depend on t, there are two parts to :
The two expressions and are actually partial derivatives, by the way. You treat one resistance as a constant while taking the derivative with respect to the other.
- Hollywood
Here's the question:
Voltage across a circuit is given by Ohm's law, V=IR, where I=the current & R= resistance.
If we place two circuits with resistance R1 and R2 in parallel their combined resistance, R, is given as
Suppose the current is 2 amps and increasing at amp/sec and is 3 ohms and increasing at 0.5 ohm/sec, while is 5 ohms and decreasing at 0.1 ohm/sec.
Calculate the rate at which the voltage is changing.
This is what I've got:
Need to find
Using the Chain Rule, I get this:
where
and
and
and
Which all comes to:
and that's as far as I've got! How do I find the change in resistance? I've tried a few ways but none of them seem satisfactory. any ideas?