(II) A galvanometer has an internal resistance of 30Ωand deflects full scale for a 50-μA current

step 1 to make an emitter a shunted register must be connected in parallel with a galvanometer. Here, s

(II) A galvanometer has an internal resistance of 30Ωand...

(II) A galvanometer has an internal resistance of 30$\Omega$ and deflects full scale for a $50-\mu$ A current. Describe how to use this galvanometer to make $(a)$ an ammeter to read currents up to $30 \mathrm{A},$ and $(b)$ a voltmeter to give a fullscale deflection of 250 $\mathrm{V}$ .

Key Concepts

Ohm’s Law and Circuit Analysis

The fundamental principles of Ohm’s law (V = IR) and series/parallel resistor networks are essential in these conversions. They allow for the proper determination of resistor values for shunt and multiplier configurations by balancing the current and voltage requirements to ensure the galvanometer operates within its safe and accurate range.

Ammeter Conversion (Shunt Resistor)

To convert a galvanometer into an ammeter for larger currents, a low resistance shunt is connected in parallel with the galvanometer. The shunt resistor bypasses most of the current such that only the small, full?scale deflection current goes through the galvanometer. By calculating the appropriate shunt resistor value through Ohm’s law and given current division, the instrument can safely measure currents much larger than its inherent sensitivity.

Galvanometer

A galvanometer is a sensitive instrument that detects and measures small electric currents via the deflection of its needle. It has a known internal resistance and a specified full?scale deflection current, which is used as the basis for converting it into an ammeter or voltmeter. Its sensitivity is crucial in determining how much additional resistance is needed in circuits to change its range.

Voltmeter Conversion (Multiplier Resistor)

For converting a galvanometer into a voltmeter, a high resistance, known as a multiplier resistor, is connected in series with the galvanometer. This series resistor drops the additional voltage so that even a high voltage applied across the combination only results in the full?scale deflection current passing through the galvanometer. The multiplier resistor is calculated based on the desired voltage range and the galvanometer’s full-scale characteristics.

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