A galvanometer reads `5*0V` at full scale deflection and is graded according to its resistance per volt at full scale deflection as `5000OmegaV^-1`. (i) How will you convert it into a voltmeter that reads `20V` at full scale deflection? (ii) Will it still be graded `5000OmegaV^-1`? (iii) Will you prefer this voltmeter to one that is graded `2000OmegaV^-1`?

Answer

`7500 Omega` resistor is to be connected in series, yes, no

Explanation

Resistance per volt at full-scale deflection in `5000 Omega V^(-1)`.
Reading of voltmeter at full-scale deflection is `5 V`. Therefore, resistance of voltmeter `G` is `5000 xx 5 = 25000 Omega`.
Also current for maximum deflection is
`I_(g) = (1V)/(5000 Omega) = 0.0002 A`
Range of voltmeter to be changed to `V = 20 V`
Now, `R = (V)/(I_(g)) - G = (20)/(0.0002) - 25,000`
`= 100,000 - 25,000 = 75,000 Omega`
Thus, `7500 Omega` is to be connected in series.
Resistance of `20 V` voltmeter is `75000 + 25000 = 100,000 Omega`. Its grading becomes `100000//20 = 5000 Omega V^(-1)`, which is same as in the earlier case. A voltmetre with grading `2000 Omega V^(-1)` will have less resistance and is, therefore , not perferred.