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Durrr i'm returded

vespertine

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im onto slope fields right now. i need insight into how slope fields can be used for physical situations as well. this next section is confusing me because of the quantity of variables and terms:

suppose a simple electric circuit contains an electromotive force (usually a battery or generator) that produces a voltage of E(t) volts (V) and a current of I(t) amperes (A) at time t. The circuit also contains a resistor with a resistance of R ohms (Ω) and an inductor with an inductance of L henries (H).

Ohm’s Law gives the drop in voltage due to the resistor as RI. The voltage drop due to the inductor is L((dI)/(dt)). One of Kirchhoff’s laws says that the sum of the voltage drops is equal to the supplied voltage E(t). Thus we have

L((dI)/(dt))+RI=E(t)

which is a first-order differential equation that models the current I at time t.

---

before we bring slope fields into this, what does all this shit mean? i feel so stupid
 
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im onto slope fields right now. i need insight into how slope fields can be used for physical situations as well. this next section is confusing me because of the quantity of variables and terms:

suppose a simple electric circuit contains an electromotive force (usually a battery or generator) that produces a voltage of E(t) volts (V) and a current of I(t) amperes (A) at time t. The circuit also contains a resistor with a resistance of R ohms (Ω) and an inductor with an inductance of L henries (H).

Ohm’s Law gives the drop in voltage due to the resistor as RI. The voltage drop due to the inductor is L((dI)/(dt)). One of Kirchhoff’s laws says that the sum of the voltage drops is equal to the supplied voltage E(t). Thus we have

L((dI)/(dt))+RI=E(t)

which is a first-order differential equation that models the current I at time t.

---

before we bring slope fields into this, what does all this shit mean? i feel so stupid
molecule
 
im onto slope fields right now. i need insight into how slope fields can be used for physical situations as well. this next section is confusing me because of the quantity of variables and terms:

suppose a simple electric circuit contains an electromotive force (usually a battery or generator) that produces a voltage of E(t) volts (V) and a current of I(t) amperes (A) at time t. The circuit also contains a resistor with a resistance of R ohms (Ω) and an inductor with an inductance of L henries (H).

Ohm’s Law gives the drop in voltage due to the resistor as RI. The voltage drop due to the inductor is L((dI)/(dt)). One of Kirchhoff’s laws says that the sum of the voltage drops is equal to the supplied voltage E(t). Thus we have

L((dI)/(dt))+RI=E(t)

which is a first-order differential equation that models the current I at time t.

---

before we bring slope fields into this, what does all this shit mean? i feel so stupid
my head is torturing me impossible to read
 
This equation describes how the current I(t) changes over time in response to the battery voltage E(t).


Basically, it says:


The rate of change of the current (how fast it’s increasing or decreasing) depends on how strong the supply voltage is, and how much resistance and inductance oppose it.
alright, this clears things up. thanks
 
im basically black when it comes to math, i don't know a thing.
L((dI)/(dt))+RI=E(t)
dI/dt -> derivative of I with respect to t (how fast the current is changing over time = amps/second for example)
(e.g derivative of distance with respect to time is dx/dt -> how fast distance [metres] are changing over time = metres/second = speed)
 
Last edited:
dI/dt -> derivative of I with respect to t (how fast the current is changing over time = amps/second for example)
(e.g derivative of distance with respect to time is dx/dt -> how fast distance [metres] are changing over time = metres/second = speed)
*kisses you on the lips*
 

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