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 ε 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 Ω, ε = 7.50 V, and r = 0.45, 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.