Electric Current — Question 3

Question 3

An asymmetric pulse train can have zero signed charge per cycle

A periodic current is +6.0 mA for 2.0 ms, then -3.0 mA for 4.0 ms. This pattern repeats without gaps.

1. Find the average signed current and average magnitude.

2. Find the total magnitude transported in 1.00 minute and the net transported charge.

Question 3 - Solution

An asymmetric pulse train can have zero signed charge per cycle

(a) Method and calculation

$$Q_+=6(2)=12\,\mathrm{\mu C},\quad Q_-=-3(4)=-12\,\mathrm{\mu C}.$$$$\overline I=0,\quad\overline{|I|}=24/6=4.00\,\mathrm{mA}.$$

(b) Interpretation and further calculation

$$Q_{\mathrm{magnitude}}=\overline{|I|}(60.0\,\mathrm s)=0.240\,\mathrm C.$$$$Q_{\mathrm{net}}=10000(Q_++Q_-)=0.$$

Physical check

The one-minute window contains an integer number of periods; average magnitude differs from magnitude of the average.