Question

An ammeter of resistance 0.6 Ω can measure current upto 1.0 A. Calculate (i) The shunt resistance required to enable the ammeter to measure current upto 5.0 A (ii) The combined resistance of the ammeter and the shunt.

Answer 1

We have, resistance of ammeter, R_A = 0.60 ohm

Maximum current across ammeter, I_A = 1.0 A

So, Voltage across ammeter, V = IR = 1.0 × 0.60 = 0.6 V

Let the value of shunt be x.

(i) Resistance of ammeter with shunt,

`R = (R_Ax)/(R_A +x) = (0.6x)/(0.6+x)`

Current through ammeter, I = 5 A.

Now,`((0.6x)/(0.6+x))xx 5 = 0.6 =>0.6x xx 5 = 0.6(0.6+x)`

`=> 3x = 0.36 +0.6x => 3x - 0.6x = 0.36`

∴`x = (0.36)/2.4 = 0.15Ω`

Therefore, the shunt resistance is 0.15 ohm.

(ii) Combined resistance of the ammeter and the shunt is given by`R = (0.6x)/(0.6 +x)`

`=> R = (0.6 xx 0.15)/(0.6 + 0.15) = 0.12Ω`