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.

Result

R2 =  80000 Ω

Solution:

$U_{ 1 } = 10 \ V \ \\ U_{ 2 } = 50 \ V \ \\ \ \\ R_{ 1 } = 2 \cdot \ 1000 \cdot \ U_{ 1 } = 2 \cdot \ 1000 \cdot \ 10 = 20000 \ Ω \ \\ U_{ 3 } = U_{ 2 }-U_{ 1 } = 50-10 = 40 \ V \ \\ \ \\ I = \dfrac{ U_{ 1 } }{ R_{ 1 } } = \dfrac{ 10 }{ 20000 } = \dfrac{ 1 }{ 2000 } = 0.0005 \ A \ \\ U_{ 3 } = I \cdot \ R_{ 2 } \ \\ \ \\ R_{ 2 } = U_{ 3 }/I = 40/0.0005 = 80000 = 80000 \ \text { Ω }$

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