In electrical measurements, a sensitive galvanometer can be converted into a voltmeter suitable for measuring potential difference by connecting which type of resistance to it?

Introduction / Context:
A galvanometer is a very sensitive instrument designed to detect and measure small currents. In practical circuits, however, we often need to measure voltage across components, not just tiny currents. By suitably modifying a galvanometer, it can be used as a voltmeter to measure potential difference across circuit elements. This question asks what kind of additional resistance must be connected, and in which configuration, to convert a galvanometer into a voltmeter correctly. Understanding this conversion is part of basic electrical instrumentation and circuit theory.

Given Data / Assumptions:
• The starting instrument is a sensitive galvanometer with a known full scale deflection current. • We wish to measure voltage (potential difference) without drawing large current from the circuit. • The options describe high or low resistances connected in series or parallel with the galvanometer. • We assume idealised conditions with linear galvanometer behaviour.

Concept / Approach:
A voltmeter should have a very high overall resistance so that it draws only a small current from the circuit, ensuring that it does not significantly disturb the voltage being measured. To convert a galvanometer to a voltmeter, we add a high resistance, called a series multiplier, in series with the galvanometer coil. This increases the effective resistance of the instrument so that even a relatively high applied voltage produces only a small current, within the galvanometer safe operating range. Connecting a low resistance or connecting resistances in parallel would change the behaviour in the wrong direction, either overloading the galvanometer or creating a device more like an ammeter or shunt.

Step-by-Step Solution:
Step 1: Recall that an ideal voltmeter must have very high resistance so that it draws minimal current from the circuit it is connected across. Step 2: Recognise that a galvanometer by itself has relatively low resistance and is sensitive to small currents. Step 3: To measure larger voltages safely, we must increase the total resistance seen by the applied voltage. Step 4: Adding a high resistance in series with the galvanometer increases the total resistance equal to galvanometer resistance plus series resistance. Step 5: For a given voltage, the current through the series combination remains small and within the galvanometer full scale range. Step 6: Conclude that a high series resistance transforms the galvanometer into a voltmeter with appropriate range and minimal circuit loading.

Verification / Alternative check:
Consider Ohms law, V = I * R. For a given voltage V to produce only a small current I through the instrument, the total resistance R must be large. If the galvanometer alone has resistance Rg and full scale current Ig, then to design a voltmeter of range V, the series resistance Rs must satisfy V = Ig * (Rg + Rs). Since V is large and Ig is small, Rs must be much larger than Rg, that is, a high resistance. Furthermore, placing this resistance in series ensures that the same small current passes through both the galvanometer and the resistor. These simple calculations confirm that the correct configuration is a high resistance in series.

Why Other Options Are Wrong:
Option A, a high resistance in parallel, would divert much of the current away from the galvanometer and complicate the relation between applied voltage and galvanometer deflection, making it unsuitable as a voltmeter arrangement. Option C, a low resistance in series, would not increase the total resistance sufficiently, allowing too much current and possibly damaging the galvanometer. Option D, a low resistance in parallel, is actually how a galvanometer is converted to an ammeter, not a voltmeter, because it allows most current to bypass the galvanometer through a shunt. These configurations therefore do not produce a proper voltmeter.

Common Pitfalls:
A frequent confusion is between the modifications needed for ammeters and voltmeters. For an ammeter, a galvanometer is shunted with a low resistance in parallel so that the overall resistance is low and large currents can be measured. For a voltmeter, the aim is the opposite: the instrument must draw very little current, so its resistance must be high. Remembering this contrast helps you quickly choose high series resistance for voltmeters and low parallel resistance for ammeters. Another pitfall is ignoring the effect of the measuring instrument on the circuit, which is crucial when designing accurate measurements.

Final Answer:
The correct choice is A high resistance in series with the galvanometer, because this configuration greatly increases the instrument resistance and allows it to measure potential difference with minimal current draw, effectively turning the galvanometer into a voltmeter.