Question

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

Answer 1

Given: An ammeter of resistance $0.6\Omega$ can measure current up to $1.0A$

To find (i) The shunt resistance required to enable the ammeter to measure current up to $5.0A$ (ii)The combined resistance of the ammeter and the shunt.

Solution:

We have, resistance of ammeter, $R_A=0.60\Omega$

Maximum current across ammeter, $I_A=1.0A$

So, voltage across the ammeter, $V=IR=1.0\times 0.60=0.6V$

Let the value of the shunt be $x$

(i) Resistanceof ammeter with shunt,

$R=\frac{R_{A}x}{R_A+x}=\frac{0.6x}{0.6+x}$

Current through ammeter, $I=5A$

Now, $\left(\frac{0.6x}{0.6+x}\right)\times 5=0.6⟹0.6x\times 5=0.6(0.6+x)⟹3x=0.36+0.6x⟹3x-0.6x=0.36$

$\therefore x=\frac{0.36}{2.4}=0.15\Omega$

Therefore, the shunt resistance is $0.15\Omega$

(ii)Combined resistance of the ammeter and the stuntis given by

$R=\frac{0.6x}{0.6+x}⟹R=\frac{0.6\times 0.15}{0.6+0.15}⟹R=\frac{0.09}{0.75}=0.12\Omega$