Solve for f and g$!!!$

Homework $7$: Ohm's Law, Kirchhoff's Rules Begin Date: $2/22/202412$:$01$:$00$ AM $--$ Due Date: $3/6/202411$:$59$:$00$ PM End Date: $3/13/202411$:$59$:$00$ PM

$(14\%)$ Problem $6$: Consider a circuit shown in the figure. Ignore the internal resistances of the batteries.

Randomized Variables

$E_1=34V$

$E_2=38V$

$R_1=6$

$R_2=4$

$R_3=1\mathrm{.}14\%$ Part $($a$)$ Express the current $I_1$ going through resistor $R_1$ in terms of the currents $I_2$ and $I_3$ going through resistors $R_2$ and $R_3.$ Use the direction of the

urrents as specified in the figure.

$I_1=I_2+I_3,$ Correct!

$14\%$ Part $($b$)$ Write the equation of potential change in loop EBAF in terms of the circuit elements.

$V_{\text{E}\text{B}\text{A}\text{F}}=E_1-I_1{R}_1-I_3{R}_3,$ Correct!

$14\%$ Part $($c$)$ Write the equation of potential change in loop DCAF in terms of the circuit elements.

$V_{\text{D}\text{C}\text{A}\text{F}}=-{}_2+I_2{R}_2-I_3{R}_3$

$14\%$ Part $($d$)$ Solve the three equations to get $I_3.$

$I_3=\frac{R_2{E}_1-R_1{E}_2}{R_1{R}_2+R_2{R}_3+R_3{R}_1}$

$14\%$ Part $($e$)$ Calculate the numerical value of $I_3$ in A$.$

$I_3=-2\mathrm{.}705$

$I_3=-2\mathrm{.}705$

$14\%$ Part $($f$)$ Calculate the numerical value of $I_2$ in A$.$

$14\%$ Part $($g$)$ Calculate the numerical value of $I_1$ in A$.$