In order to triple the range of a voltmeter in a circuit, we need to adjust the resistance value. Let's analyze the situation step by step:

1. Understanding the Range of a Voltmeter:
A voltmeter is a measuring instrument used to measure the potential difference or voltage across a component or set of components in a circuit. The range of a voltmeter refers to the maximum voltage it can measure accurately. For example, if a voltmeter has a range of 0-10V, it can measure voltages up to 10 volts.

2. Relationship between Resistance and Voltage Measurement:
The range of a voltmeter is determined by the internal resistance it possesses. The higher the internal resistance, the lower the range of the voltmeter. Conversely, the lower the internal resistance, the higher the range of the voltmeter. This is because the internal resistance of the voltmeter forms a voltage divider with the component being measured, affecting the voltage reading.

3. Tripling the Range:
To triple the range of a voltmeter, we need to decrease its internal resistance. Let's assume the original internal resistance of the voltmeter is 'R'.

4. Applying the Ratio:
To triple the range, the new internal resistance ('R_new') should be three times smaller than the original internal resistance ('R'). Mathematically, we can express this as:

R_new = R/3

5. Expressing the Resistance Value:
Now, we need to express the resistance value in terms of the given options. Let's examine the options provided:

a) 3R: This option suggests increasing the resistance by a factor of 3, which is the opposite of what we need to do.
b) R/2: This option suggests reducing the resistance by half, which is again not in line with our objective.
c) 2R: This option suggests doubling the resistance, which is also not what we require.
d) 4R: This option suggests increasing the resistance by a factor of 4, which is the opposite of what we need to do.

6. Identifying the Correct Option:
Based on the above analysis, option 'C' (2R) is the correct answer. Reducing the internal resistance to 2R will triple the range of the voltmeter, as indicated in step 4.

By adjusting the resistance value to 2R, the voltmeter will have a lower internal resistance, allowing it to measure higher voltages accurately and extend its range.