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Ohm's Law is a fundamental principle used to understand the relationship between voltage, current, and resistance in an electrical circuit. According to this law, the voltage (V) across a resistor is the product of the current (I) passing through it and the resistance (R) of the resistor. This can be mathematically expressed as:\[ V = IR \]This simple formula is the cornerstone for analyzing DC circuits. By knowing any two of the three quantities, the third can be easily calculated.
Ohm's Law applies to both small-scale components like milliammeters and large-scale electrical systems. In this conversation problem, Ohm’s Law is used to calculate the voltage across the milliammeter at its full scale deflection. Given its resistance and full-scale current, the method determines the voltage necessary to achieve this deflection.

When resistors are connected in series, the total resistance of the circuit is simply the sum of all individual resistances. In the context of converting a milliammeter into a voltmeter, series resistance is crucial.
The original milliammeter has a certain intrinsic resistance, which must be accounted for when adding external resistance to achieve a new desired full-scale reading.

• The intrinsic resistance is given, in this case, as \(12\, \Omega\).
• The full scale deflection current of the milliammeter is \(0.01\, \text{A}\).
• To convert the device into a voltmeter with a different full-scale voltage (e.g., \(3\, \text{V}\)), additional external resistance is used.

In our exercise, this additional resistance ensures that the correct voltage is measured when the desired full-scale current flows through. Using Ohm's Law, the total resistance required can be determined, and the additional series resistance \(R_s\) is calculated to make up the difference.

Full scale deflection refers to the condition when the needle of an analog meter (like a milliammeter or voltmeter) moves to its maximum position, indicating the maximum measurable current or voltage.
To set an instrument to give a full-scale deflection at a particular voltage or current means adjusting either the internal or external conditions such that the specified measurement causes the needle to reach the end of the measurement scale.

• For a milliammeter, this is achieved when the designated current value (such as \(0.01\, \text{A}\)) flows through it.
• Once a milliammeter is converted to measure voltage, the full-scale deflection voltage is the total of the voltage produced across all resistances in the circuit.

In the problem discussed, the instrument needs to give a full-scale reading at \(3\, \text{V}\). By using Ohm's Law and its application with series resistance, the problem calculates the necessary additional resistance to make sure that the full-scale deflection occurs accurately.