Question

An ammeter of resistance 1 Ω can measure current up to 1.0 A (i) What must be the value of the shunt resistance to enable the ammeter to measure up to 5.0 A? (ii) What is the combined resistance of the ammeter and the shunt?

Answer 1

We have, Resistance of ammeter, R_A = 1 ohm

Maximum current across ammeter, I_A = 1.0 A

So, Voltage across ammeter, V =

Let the value of shunt be x, then

(i) Resistance of ammeter with shunt, `R = (R_Ax)/(R_A+x) = x/(1+x)`

Current through ammeter, I = 5 A.

Now `x/(1+x) xx 5 = 1.0 ⇒ x xx 5 = 1 + x ⇒ 4x = 1 ⇒ x= 0.25`

Thus the shunt resistance is 0.25 ohm.

(ii) Combined resistance of the ammeter and the shunt

`R = x/(1+x) ⇒ R = (1 xx 0.25)/(1 +0.25)⇒ R = (0.25)/(1.25)0.2 \text { ohm}`