Advertisements
Advertisements
Question
An ammeter of resistance 0.80 Ω can measure current up to 1.0A.
(i) What must be the value of shunt resistance to enable the ammeter to measure current up to 5.0 A?
(ii) What is the combined resistance of the ammeter and the shunt?
Solution
We have, resistance of ammeter, RA = 0.80 ohm and maximum current across ammeter, IA = 1.0 A.
So, voltage across ammeter, V = IR = 1.0 × 0.80 = 0.8 V.
Let the value of shunt be x.
(1) Resistance of ammeter with shunt, `R = (R_Ax)/(R_A + x) =(0.8x)/(0.8 +x)`
Current through ammeter, I = 5 A.
`∴ ((0.8x)/(0.8 +x)) xx 5 = 0.8 =>0.8x xx 5 = 0.8 (0.8 +x)=> 4x = 0.64 + 0.8x`
`∴ = (0.64)/3.2 = 0.2`
Thus, the shunt resistance is 0.2 ohm.
(ii) Combined resistance of the ammeter and the shunt, `R =(0.8x)/(0.8 +x) = (0.8 xx 0.2)/(0.8 +0.2) = 0.16/1 = 0.16 \text { ohm} `
