Exercise E10 Determining the Current from Charge per Time
Two objects experience a charge increase per time. In the Abbildung 1 one can see these increases in the charge per time.
1. Determine the currents $I_1$ and $I_2$ for the two objects from the $Q$-$t$-diagram Abbildung 1 and plot the currents into a new diagram.
- Have a look how much increase $\Delta Q$ per time duration $\Delta t$ is there for each object.
- For this choose a distinct time period, e.g. between $0~\rm s$ and $20~\rm s$.
- The current is then given as the change in charge per time: $I= {{\Delta Q}\over{\Delta t}}$
2. How can the current be determined, when the charge increase on an object changes non-linearly?
A non-linear charge increase leads to a non-constant current.
For a non-constant current, one has to use the time derivative of the charge $Q$ to get the current $I$.
So, the formula $I= {{{\rm d} Q}\over{{\rm d} t}}$ has to be used instead of $I= {{\Delta Q}\over{\Delta t}}$.
For a non-constant current, one has to use the time derivative of the charge $Q$ to get the current $I$.
So, the formula $I= {{{\rm d} Q}\over{{\rm d} t}}$ has to be used instead of $I= {{\Delta Q}\over{\Delta t}}$.