An instrument with an internal resistance of 100 Ω and a full-scale current of 1 mA is to be converted into a DC voltmeter with range of 0 V - 500 V. Find the value of the resistance used as a multiplier.  

The correct answer is option 3):(499900 Ω)

Concept:

The ratio between the two voltmeters can be

\(V_1 \over V_2\) = \(R_1 \over R_2\)

V₁  is the Intial voltage range of the voltmeter

V₂ is the final voltage range of the voltmeter after adding multiplier resistance

R₁ is the initial Resistance

R₂ is the final Resistance 

Calculation:

Given

The full-scale current of 1 mA 

R₁ = 100 Ω

V₂ = 500 V

​\(V_1 \over V_2\) = \(R_1 \over R_2\)​

V₁ ​= i × R₁​

=1×10⁻³×100 = 0.1

\(0.1 \over 500\) = \(100 \over(x+ 100)\)

x + 100 = \(100 \times 500 \over 0.1\)

x = 499900 Ω