Electric Current — Question 8

Question 8

A charge budget limits the duty cycle of intermittent operation

An ideal charge reservoir has 2.00 Ah usable capacity. A device draws 5.00 mA at rest and 205 mA during a 3.00 s active interval every 60.0 s. Treat the currents as prescribed.

1. Find the average current and ideal operating time.

2. Find the largest active fraction that permits at least 100 h of operation.

Question 8 - Solution

A charge budget limits the duty cycle of intermittent operation

(a) Method and calculation

$$f=3/60=.0500,\quad\overline I=5(1-f)+205f=15.0\,\mathrm{mA}.$$$$t=2.00\,\mathrm{Ah}/.0150\,\mathrm A=133.3\,\mathrm h.$$

(b) Interpretation and further calculation

$$\overline I\le 2.00/100=.0200\,\mathrm A.$$$$.005+.200f\le.020\Rightarrow f\le.0750.$$

Physical check

Ampere-hours measure charge, not energy; voltage and nonideal battery effects are excluded.