5. (20 points) A voltmeter connected to the terminals of a current source with an EMF of $12 \mathrm{~V}$ shows a voltage $U=9 \mathrm{~V}$. Another identical voltmeter is connected to the terminals of the source. Determine the readings of the voltmeters. (The internal resistance of the source is non-zero, the resistance of the voltmeters is finite).
5. According to Ohm's law for a segment of a circuit and for a closed circuit

In the first case

$U_{1}=I_{1} R_{\mathrm{v}}=\frac{\varepsilon R_{\mathrm{v}}}{r+R_{\mathrm{v}}}=\frac{\varepsilon}{\left(\frac{r}{R_{\mathrm{v}}}+1\right)} \rightarrow \frac{r}{R_{\mathrm{v}}}=\frac{\varepsilon-U_{\mathrm{v}}}{U_{1}}$

In the second case

$U_{2}=\frac{I_{2}}{2} R_{\mathrm{v}}=\frac{\varepsilon R_{\mathrm{v}}}{2\left(r+\frac{R_{\mathrm{v}}}{2}\right)}=\frac{\varepsilon}{2\left(\frac{r}{R_{\mathrm{v}}}+\frac{1}{2}\right)}$

$U_{2}=\frac{\varepsilon U_{1}}{2 \varepsilon-U_{1}}=7.2 \mathrm{~V}$.

(20 points)