$E=10V$

$R_1=120$

$R_2=140$

$R_3=120$

$R_4=120$

i$)$ Find the equivalent resistance of the DC circuit by identifying resistors connected in series or parallel and using the appropriate formula.

ii$)$ Calculate the source current in mA to $3$ decimal places.

iii$)$ Evaluate $V_1,V_3,I_1$ and $I_3.$

iv$)$ What is the voltage between a and $b.$

$($b$)5$ kW of power is input to the gear train from the hydro blades. If the efficiency of the gear train is $98\%,$ and the overall output power is $4361$ W $,$ calculate i$)$ the input power to the generator, ii$)$ the efficiency of the generator, and the overall hydro system efficiency.

$(8$ marks$)$

$($c$)$ An electric car uses a $7\mathrm{.}4$ kW power source to charge and it takes $6$ hours to fully charge the battery. Assuming a constant power transfer, how many a$)$ kWh and b$)$ Joules does it take to charge the battery? What is the cost to charge by day at $0\mathrm{.}43$ and by night at $0\mathrm{.}23.$

$(8$ marks$)$