How to Convert a 8V Voltmeter to 20V with Same Ohms per Volt Rating?

[kihr]

Homework Statement

A voltmeter reads 8V at full scale deflection, and is graded according to its resistance per volt at full scale deflection as 5000 ohms / volt. How will you convert it into a voltmeter that reads 20V at full scale deflection? Will it still be graded as 5000 ohms / volt.? Will you prefer this voltmeter to one that is graded ats 2000 ohms /volt?

Homework Equations

Application of Ohm's Law

The Attempt at a Solution

Let R = voltmeter resistance
I = current through voltmeter for full scale deflection

If the voltmeter has to read 20V at full scale deflection, we need an additional resistance r in series with it. Thus

8/R = 20/R+r
R = 5000 *8 (since the voltmeter is graded as 5000 ohms/V for full scale deflection
of 8V)
1/5000 = 20/40000 +r
r= 60000 ohms
The above has been calculated using the voltmeter grading as 5000 ohms /V.
I need some clues to proceed further with the next part of the question as I am not sure as to whether my way of looking at the voltmeter grading is correct or not.

 

[ehild]

Your solution is correct, go ahead.

ehild

 

[kihr]

OK. Now if we consider a voltmeter grading of 2000 ohms / V, we get the value of external resistance as 24000 ohms. This being lower than the earlier value of 60000 ohms, is less preferred because the higher the resistance, the less the current drawn by the voltmeter. Trust this solution is in order. Please advise. Thanks.

 

[ehild]

The ohm/volt value means reciprocal current, the reciprocal of the current which is allowed to flow through the voltmeter at full-scale deflection. Does it change if you connect a series resistance to the voltmeter?
Less ohm/volt means higher allowed current at the same full-scale voltage, and lower resistivity of the voltmeter. As you said, this is less preferred in measuring voltage in a circuit, as a lower-resistivity voltmeter would influence the currents in the circuit at higher extent as a high-resistivity meter.

ehild

 

[kihr]

Thanks a lot for your help.