# Help me solve this differential equation (Capacitor Charging)

• thomas49th
In summary, a differential equation is used to relate a function to its derivatives and is commonly used in science and engineering. For capacitor charging, the differential equation Q = CV is used and the initial conditions of the charge and voltage are needed to solve it. The method of separation of variables can be used to solve the equation and this allows us to understand and predict the behavior of a capacitor in an electric circuit.

#### thomas49th

I'm trying to solve this:

$$E = R\frac{dQ}{dt} + \frac{Q}{C}$$

from here
http://physics.bu.edu/~duffy/semester2/c11_RC.html
You might recognize this as the charging equation for a capacitor

I'm guessing I need to try and get (1/q)dQ or similar somewhere to get the lnQ

but I cannot seem to get the right manipulation

Thanks
Thomas

Last edited:
for example,
divide the equation by dQ and write the terms with dQ and dt each to another side of the equation. Integrate both sides and you will be able to find Q(t)

## 1. What is a differential equation?

A differential equation is an equation that relates a function to its derivatives. It is commonly used in science and engineering to model natural phenomena and physical processes.

## 2. How is a capacitor charging described by a differential equation?

A capacitor charging is described by the differential equation Q = CV, where Q is the charge on the capacitor, C is the capacitance, and V is the voltage across the capacitor. This equation shows the relationship between the rate of change of charge and the voltage across the capacitor.

## 3. What are the initial conditions needed to solve a differential equation for capacitor charging?

The initial conditions needed to solve a differential equation for capacitor charging are the initial charge on the capacitor (Q₀) and the initial voltage across the capacitor (V₀). These values are typically given at t = 0, when the charging process begins.

## 4. How is a differential equation solved for capacitor charging?

To solve a differential equation for capacitor charging, we can use the method of separation of variables. This involves isolating the variables on opposite sides of the equation and integrating both sides with respect to time. The resulting equation can then be solved for the unknown variable.

## 5. What is the significance of solving a differential equation for capacitor charging?

Solving a differential equation for capacitor charging allows us to understand and predict the behavior of a capacitor in an electric circuit. It helps us determine the charge and voltage across the capacitor at any given time, which is crucial in designing and analyzing electronic systems.