Unlike the idealized ammeter described in Section 25.4,

Chapter 25, Problem 25.75

(choose chapter or problem)

A Nonideal Ammeter. Unlike the idealized ammeter described in Section 25.4, any real ammeter has a nonzero resistance. (a) An ammeter with resistance \(R_A\) is connected in series with a resistor R and a battery of emf \(\mathcal{E}\) and internal resistance r. The current measured by the ammeter is \(I_A\). Find the current through the circuit if the ammeter is removed so that the battery and the resistor form a complete circuit. Express your answer in terms of \(I_A\), r, \(R_A\), and R. The more “ideal” the ammeter, the smaller the difference between this current and the current \(I_A\). (b) If \(R=3.80 \ \Omega, \ \mathcal{E}=7.50 \ \mathrm{V}\), and \(r=0.45\ \Omega\), find the maximum value of the ammeter resistance \(R_A\) so that \(I_A\) is within 1.0% of the current in the circuit when the ammeter is absent. (c) Explain why your answer in part (b) represents a maximum value.