- Joined
- Aug 17, 2025
- Messages
- 3,390
- Solutions
- 2
- Time Online
- 8d 8h
- Reputation
- 10,602
- Location
- Not the United Kingdom
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
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