Solving Equation: V0 - dQ(t)/dt * R(t) - Q(t)/C(t)

  • Thread starter Mica
  • Start date
C(t).In summary, the conversation is about solving a linear differential equation with variable coefficients and using Laplace Transform to find a formal solution. The equation in question is V0 - dQ(t)/dt * R(t) - Q(t)/C(t) = 0 and the hint given is to try solving the homogeneous solution first.
  • #1
Mica
32
0
Hi,

Can someone give me a hint for solving this equation?

V0 - dQ(t)/dt * R(t) - Q(t)/C(t) = 0

Thanks,

Mica
 
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  • #2
What have you done so far? Have you tried solving the homogeneous solution first?
 
  • #3
Sorry, I have long time that I did not solve a differencial equation. Can you give me its form?

thanks,

Mica
 
  • #4
Exponential decay.
 
  • #5
What you have is a linear differential equation with variable coefficients. The solution depends strongly upon what Q(t) and R(t) are. You might be able to use Laplace Transform to write a "formal" solution in terms of integrals of Q(t) and R(t)
 

1. What is the purpose of solving this equation?

The purpose of solving this equation is to determine the voltage (V0) at a given time interval by taking into account the change in charge (dQ/dt) and the resistance (R) and capacitance (C) of the system.

2. How is this equation derived?

This equation is derived from Ohm's law (V = IR) and the formula for capacitance (C = Q/V). By substituting V=IR into the formula for capacitance, we can solve for V0 by considering the change in charge (dQ/dt) over time.

3. What are the units for each variable in this equation?

V0 is measured in volts (V), dQ/dt is measured in amperes per second (A/s), R is measured in ohms (Ω), and C is measured in farads (F).

4. Are there any assumptions made when using this equation?

Yes, this equation assumes that the system is in a steady state, meaning that the voltage, current, and charge are not changing over time. It also assumes that the resistance and capacitance values are constant throughout the system.

5. How is this equation used in practical applications?

This equation is commonly used in circuit analysis and design to determine the voltage at a specific point in time. It is also used in fields such as electronics, electrical engineering, and physics to model and analyze systems with capacitors and resistors.

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