# Variable Capacitor

Linear time-varying capacitor

**Library:**Simscape / Electrical / Passive

## Description

The Variable Capacitor block represents a linear
time-varying capacitor. The block provides two options for the relationship between the
current *i* through the capacitor and the voltage *v*
across the device when the capacitance at port **C** is
*C*. The **Equation** parameter determines which
of the following equations the block uses:

$$i=C\frac{dv}{dt}$$

Use the preceding equation when the capacitance is defined as the local gradient of the charge-voltage curve for a given voltage:

$$C(v)=\frac{dQ(v)}{dv}$$

$$i=\frac{dC}{dt}v+C\frac{dv}{dt}$$

Use the preceding equation when the capacitance is defined as the ratio of the charge

*Q*to the steady-state voltage:$$C(v)=\frac{Q(v)}{v}$$

The block includes a resistor in series with the variable capacitor. You can use this resistor to represent the total ohmic connection resistance of the capacitor. You may need to use this resistor to prevent numerical issues for some circuit topologies, such as where a Variable Capacitor block is connected in parallel with another capacitor block that does not have a series resistance.

## Ports

### Input

### Conserving

## Parameters

## Model Examples

## Extended Capabilities

## Version History

**Introduced in R2008a**