22P2Q07

7ai)

Cost for ICE:  

\displaystyle \frac{\$80}{800}=\$latex \displaystyle 0.10\text{k}{{\text{m}}^{-1}}

Cost for EV:   

\displaystyle \frac{72\text{ kWh}\times \$0.23}{400}=\$latex \displaystyle 0.0414\text{k}{{\text{m}}^{-1}}

\displaystyle \text{Ratio}=0.0414\div 0.10=0.414

7aii)

The range of 400 km is longer the typical travelling distance of 290 km per week.

7bi)

“The home battery charger uses an a.c. supply to provide 7.2 kW with an equivalent direction current of 32 A”.

\displaystyle \begin{aligned}   (P&=VI) \\  7200&=V(32) \\  V&=225\text{ V} \end{aligned}

The 2.0 A limit means \displaystyle 32\div 2=16parallel branches.

The 3.0 V limit means \displaystyle 225\div 3=75 cells in series in each branch.

Number of cells \displaystyle =16\times 75=1200

7bii)

Every hour of charging provides 40 km of range.

7biii)

Every kg of battery stores 141 Wh of energy.

7biv)

\displaystyle 72000\text{ Wh}\div 141\text{ Wh k}{{\text{g}}^{-1}}=511\text{ kg}

7bv)

Placing the heavy battery below the floor lowers the centre of gravity of the vehicle, thus improving the stability of the vehicle.

7ci)

COMMENT: You are expected to use the correct circuit symbol for a diode.

7cii)

7d)

\displaystyle \begin{aligned}   (KE&=\frac{1}{2}m{{v}^{2}}) \\  E&=\frac{1}{2}(1685){{(25)}^{2}} \\  &=526.6\text{ kJ} \end{aligned}

\displaystyle \frac{526.6\text{ kJ}}{72\text{ kWh}\times 3600}\times 400=0.813\text{ km}

7ei)

A DC voltage would produce a constant magnetic field. Electromagnetic induction requires a changing magnetic flux linkage.

7eii)

If too far away, the (rate of change of) magnetic flux linkage experienced by the EV coil will be too small, resulting in negligible induced voltage.

COMMENT: The larger the (rate of change of) magnetic flux linkage, the stronger the induced voltage. (\displaystyle \varepsilon =-\frac{d\Phi }{dt})

7fi)

Torque of a couple,

\displaystyle \begin{aligned}   \tau &={{F}_{B}}\times d \\  &=N\times (BIL)\times d \\  &=BANI \\   \\  395&=B(6.1\times {{10}^{-3}})(1200)(96) \\  B&=0.562\text{ T} \end{aligned}

7fii)

In the original arrangement, the torque varies sinusoidally as the coil rotates. This arrangement produces a more constant torque and thus smoother rotation of the motor..

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