Answer to Question #298159 in Electric Circuits for cols

Question

A galvanometer with a resistance of 15.0Ω gives a full-scale reading for current of 3.0 A. What shunt resistance is needed to convert this into an ammeter with a 30.0 A full-scale reading?

Answer 1

According to Ohm's law, the currents in parallel circuits are inversely proportional to the resistances:

$\frac{I_a}{I_{sh}}=\frac{R_{sh}}{R_a}$,

where $I_a$ - the current through the ammeter,

$I_{sh}$ - the current through the shunt resistance,

$R_a$ - the resistance of the ammeter,

$R_{sh}$ - the shunt resistance.

The current through the shunt resistance:

$I_{sh}=I_{fs}-I_a$ ,

where $I_{fs}$ - the current of full-scale reading.

So,

$R_{sh}=R_a\frac{I_a}{I_{fs}-I_a}=15\frac{3}{30-3}=1.67\space Ohm$.