(Solved): A circuit is constructed with six resistors and two batteries as shown. The battery voltages are v1 ...

A circuit is constructed with six resistors and two batteries as shown. The battery voltages are $v_1=18\mathrm{V}$ and ${\mathrm{V}}_2=12\mathrm{V}$. The positive terminals are indicated with a + sign, The values for the resistors are: $R_1=R_5=53?,R_2=R_6=98?R_3=42?$, and $R_4=110?$. The positive directions for the currents $I_1,I_2$ and $I_3$ are indicated by the directions of the arrows. 1) What is $V_4$, the magnitude of the voltage across the resistor $R_4$ ? $\mathrm{V}$ 2) What is $I_3$, the current that flows through the resistor $R_3$ ? A positive value for the current is defined to be in the direction of the arrow. A 3) What is $I_2$, the current that flows through the resistor $R_2$ ? A positive value for the current is defined to be in the direction of the arrow. A 4) What is $I_1$, the current that flows through the resistor $R_1$ ? A positive value for the current is defined to be in the direction of the arrow. A 5) What is $V(a)?V(b)$, the potential difference between the points $a$ and $b$ ?