Ammeter Shunt and Voltmeter Multiplier Resistance Ratio

When extending the range of measuring instruments like ammeters and voltmeters, we use external resistances. For ammeters, a shunt resistance is connected in parallel, and for voltmeters, a multiplier resistance is connected in series.

Understanding Ammeter Shunt Resistance

• An ammeter shunt is a low-resistance path connected in parallel with the ammeter coil.
• Its purpose is to bypass a large portion of the main current, allowing only a small, proportional current to flow through the ammeter's internal resistance.
• To achieve this bypass effect, the shunt resistance must be significantly lower than the internal resistance of the ammeter. Typically, shunt resistances are very small values (in ohms or milliohms).

Understanding Voltmeter Multiplier Resistance

• A voltmeter multiplier is a high-resistance component connected in series with the voltmeter coil.
• Its purpose is to drop a large portion of the total voltage being measured, ensuring that only a small, proportional voltage is applied across the voltmeter's internal resistance.
• To achieve this voltage division effect, the multiplier resistance must be significantly higher than the internal resistance of the voltmeter. Typically, multiplier resistances are very large values (in kilohms or megohms).

Calculating the Ratio of Resistances

The question asks for the ratio:

\(\rm \frac{resistance \ of \ ammeter \ shunt }{resistance \ of \ voltmeter \ multiplier}\)

Based on the roles of these components:

• The resistance of the ammeter shunt is a very low value.
• The resistance of the voltmeter multiplier is a very large value.

Therefore, the ratio of a very low value to a very large value will result in a very small overall value. For example, a milliohm value divided by a megohm value would yield a very small fraction.

Thus, the ratio \(\rm \frac{resistance \ of \ ammeter \ shunt }{resistance \ of \ voltmeter \ multiplier}\) is a very small value.