Effective and mean voltage

A voltage divider consisting of resistors R1 = 103000 Ω and R2 = 197000 Ω is connected to the ideal sine wave voltage source. R2 is connected to a voltmeter, which measures the mean voltage and has an internal resistance R3 = 200300 Ω. The measured value is 109 V. Determine the effective source voltage.

Final Answer:

U₁ =  246.6253 V

Step-by-step explanation:

$$\begin{gathered} R_1=103000\Omega \\ {R}_2=197000\Omega \\ {R}_3=200300\Omega \\ {U}_2=109\text{V} \\ {U}_{21}=\pi \cdot U_2/2=3.1416\cdot 109/2\doteq 171.2168\text{V} \\ {U}_{22}=U_{21}/\sqrt{2}=171.2168/\sqrt{2}\doteq 121.0686\text{V} \\ {I}_3=U_{22}/R_3=121.0686/200300\doteq 0.0006\text{A} \\ {I}_2=U_{22}/R_2=121.0686/197000\doteq 0.0006\text{A} \\ {I}_1=I_2+I_3=0.0006+0.0006\doteq 0.0012\text{A} \\ {U}_{11}=I_1\cdot R_1=0.0012\cdot 103000\doteq 125.5567\text{V} \\ {U}_1=U_{11}+U_{22}=125.5567+121.0686=246.6253\text{V} \end{gathered}$$

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