Question

A basic 1’ Arsonval movement with internal resistance R_m = 100 Ω and full scale deflection current If = 1 mA is to be converted into a multi range d.c. voltmeter with voltage ranges of 0−10 V, 0−50 V, 0−250 V and 0−500 V. Find the values of suitable multipliers.

Answer 1

Full-scale voltage drop = (1 mA) (100 Ω) = 100 mV. Hence, sensitivity of this movement is 100/100 × 10⁻³ = 1 kΩ/V. 

(i) 0−10 V range 

Total resistance required = (1 kΩ/V) (10 V) = 10 kΩ. Since meter resistance is 1 kΩ additional series resistance required for this range R₁ = 10 − 1 = 9 kΩ 

(ii) 0-50 V range 

R_T = (1 kΩ/V) (50 V) = 50 kΩ; R₂ = 50 − 9 − 1 = 40 kΩ 

(iii) 0−250 V range 

R_T = (1 kΩ/V) (250 V) = 250 kΩ; R₃ = 250 − 50 = 200 kΩ 

(iv) 0−500 V range 

R_T = (1 kΩ/V) (500 V) = 500 kΩ ; R₄ = 500 − 250 = 250 kΩ