A research team is building a low-current sensor network and must ensure that their ammeters do not significantly disturb the currents they are intended to measure. Each ammeter has an internal resistance Rint. Consider a single branch of resistance R that carries an ideal current Itrue before an ammeter is inserted in series.
Respond to the prompts below.
(a) Draw and verbally describe an equivalent circuit model that represents the branch both before and after the ammeter is inserted.
(b) Derive an algebraic expression for the measured current Imeas in terms of Itrue, R, and Rint.
(c) Using your result from part (b), obtain an expression for the percentage error ε=Itrue∣Imeas−Itrue∣×100%.
(d) For a branch resistance of R=12Ω, determine the maximum allowable Rint if the experimenters require ε<1.0%. State your reasoning clearly.