"Pumping" Charges — Question 8

Question 8

Finite energy-conversion power limits a charge pump operating at fixed voltage

A source converts mechanical power $P_m=80.0$ W into electrical output with efficiency eta=.750. It maintains terminal voltage V=24.0 V within its operating range.

1. Find its maximum steady current and charge delivered in 30.0 s.

2. If the demanded current is 3.00 A at the same voltage, find required mechanical power and decide whether the specified source can sustain it.

Question 8 - Solution

Finite energy-conversion power limits a charge pump operating at fixed voltage

(a) Method and calculation

$$P_e=\eta P_m=60.0\,\mathrm W,\quad I_{\max}=P_e/V=2.50\,\mathrm A.$$$$Q=I_{\max}t=(2.50)(30.0)=75.0\,\mathrm C.$$

(b) Interpretation and further calculation

$$P_{m,\mathrm{required}}=VI/\eta=(24.0)(3.00)/.750=96.0\,\mathrm W.$$$$96.0>80.0\Rightarrow\text{the specified voltage and current cannot both be sustained}.$$

Physical check

An ideal voltage description must still be restricted to the physical energy-conversion capacity of a real source.