(Solved): The figure shows a circuit with two batteries and three resistors. Determine the magnitude of the ...

The figure shows a circuit with two batteries and three resistors. Determine the magnitude of the current through resistor \( R_{2} \) if the battery emfs and resistances are: \( \varepsilon_{1}==13 \mathrm{~V}, \varepsilon_{2}=20 \mathrm{~V}, R_{1}=10 \) \( 2, R_{2}=2 \Omega \), and \( R_{3}=5 \Omega \) [Tip: Start by using Kirchhoff's node and/or loop rules to write a system of three equations for the three branch currents. Then solve the system either analytically or using a solver like Matlab, etc.]