A moving-coil meter produces a full-scale deflection for a...

A moving-coil meter produces a full-scale deflection for a current of $50 \mu \mathrm{A}$ and has a resistance of $10 \Omega$. Select a series resistor to turn this device into a voltmeter with an f.s.d. of $10 \mathrm{~V}$.

Key Concepts

Series Resistor for Voltage Measurement

When converting a current meter to a voltmeter, a series resistor is added so that under full-scale conditions, the voltage drop across the combination of the meter and resistor equals the desired full-scale voltage. This additional resistance ensures that only the appropriate fraction of the voltage appears across the sensitive meter while the rest is dropped across the series resistor, allowing for safe and accurate voltage measurement.

Ohm’s Law

Ohm’s Law, which states that the voltage across a resistor is proportional to the current flowing through it (V = IR), is critical in determining the relationship between current, voltage, and resistance in electrical circuits. This principle is used to calculate the required additional resistance needed when adapting a current meter to measure voltage.

Full-Scale Deflection

The full-scale deflection refers to the maximum current that a meter can handle before it reaches its full range of motion. Understanding full-scale deflection is crucial because it dictates both the sensitivity and scalability of the instrument when converting it to measure other electrical quantities, such as voltage.

Moving-Coil Meter

This is an electromechanical instrument that converts an electric current into a mechanical deflection. Its operation is based on the interaction between a magnetic field and the current passing through a coil, which causes the needle to move proportionally to the current. This principle is foundational for analog measurement devices.

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