Two ammeters, 1 and 2

PHYSICS · Single correct · A Level · Physics · Electricity · Electricity

Problem

Two ammeters, 1 and 2, have different internal resistances: r1r_1 (known) and r2r_2 (unknown). Each ammeter has scale such that the angular deviation of the needle from zero is proportional to the current. Initially, the ammeters are connected in series and then to a source of constant voltage. The deviations of the needles of the ammeters are θ1\theta_1 and θ2\theta_2, respectively. The ammeters are then connected in parallel and then to the same voltage source. This time, the deviations of the needles are θ1′\theta'_1 and θ2′\theta'_2, respectively. r2r_2 in terms of r1r_1, θ1\theta_1, θ2\theta_2, θ1′\theta'_1 and θ2′\theta'_2 is. (a) r1θ1θ1′θ2θ2′r_1\frac{\theta_1\theta'_1}{\theta_2\theta'_2} (b) r1θ2θ1′θ1θ2′r_1\frac{\theta_2\theta'_1}{\theta_1\theta'_2} (c) r1θ2θ2′θ1θ1′r_1\frac{\theta_2\theta'_2}{\theta_1\theta'_1} (d) r1θ1θ2′θ2θ1′r_1\frac{\theta_1\theta'_2}{\theta_2\theta'_1}

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