Voltmeter range

We have a voltmeter which in the original set measures voltage to 10V. Calculate the size of the ballast resistor for this voltmeter, if we want to measure the voltage up to 50V. Voltmeter's internal resistance is 2 kiloohm/Volt.

Correct result:

R₂ =  80000 Ω

Solution:

$$\begin{gathered} U_1=10\text{ V } \\ {U}_2=50\text{ V } \\ {R}_1=2\cdot 1000\cdot U_1=2\cdot 1000\cdot 10=20000\mathrm{\Omega } \\ {U}_3=U_2-U_1=50-10=40\text{ V } \\ I={\displaystyle \frac{U_1}{R_1}}={\displaystyle \frac{10}{20000}}={\displaystyle \frac{1}{2000}}=0.0005\text{ A } \\ {U}_3=I\cdot R_2 \\ {R}_2=U_3\mathrm{/}I=40\mathrm{/}0.0005=80000\mathrm{\Omega } \end{gathered}$$

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