4. In the circuit shown in the diagram, the EMF of the source $\varepsilon=69 \mathrm{~V}, R_{1}=R=10 \mathrm{~\Omega}, R_{2}=3 R$, $R_{3}=3 R, R_{4}=4 R$. The internal resistance of the source and the resistance of the ammeter can be neglected.
1) Find the current through the resistor $R_{1}$.
2) Find the current through the ammeter.

![](https://cdn.mathpix.com/cropped/2024_05_06_0b0ef98a4ab1cfc2e4dfg-2.jpg?height=611&width=691&top_left_y=1668&top_left_x=1231)
4. $R_{13}=\frac{R_{1} R_{3}}{R_{1}+R_{3}}=\frac{3}{4} R ; \quad R_{24}=\frac{R_{2} R_{4}}{R_{2}+R_{4}}=\frac{12}{7} R ;$

$U_{13}=\frac{\varepsilon R_{13}}{R_{13}+R_{24}}=\frac{7}{23} \varepsilon ; \quad I_{1}=\frac{U_{13}}{R}=\frac{7}{23} \frac{\varepsilon}{R}=2.1 \mathrm{~A}$

$U_{24}=\varepsilon-U_{13}=\frac{16}{23} \varepsilon ; \quad I_{2}=\frac{U_{24}}{3 R}=\frac{16}{69} \frac{\varepsilon}{R}=1.6 \mathrm{~A}$

$I=I_{1}-I_{2}=\frac{5}{69} \frac{\varepsilon}{R}=0.5$ A (current flows downwards)

![](https://cdn.mathpix.com/cropped/2024_05_06_4d7aec0c8bbef904a8ecg-3.jpg?height=363&width=446&top_left_y=2137&top_left_x=1476)