A small electric car overcomes a 250 N friction force between the road and its wheel when traveling at 30 kmh –1 . The electric motor is powered by ten 12 V batteries connected in series and is directly coupled to the wheels whose diameters are 50 cm. The 10 cm × 15 cm rectangular motor coils have 300 turns and rotate in a 0.60 T magnetic field. You may assume that the geometry of the motor is such that the magnetic field is always parallel to the plane of the coils.
(i) How much current does the motor draw to produce the required torque?
Text Solution
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Ans.
(i)
Sol. Torque due to frictional force F
τ = FR
NIAB = FR
I = 
I = 23.15 amp
(ii)
Sol. Back emf = NAB ω sin ω t
Here sin ω t = 1
∴ E = NAB ω
ω = 
∴ E = 
E = 90 volt
(iii)
Sol. Power delivered by battery = V × I
= 10 × 12 × 23
= 2760
Power dissipated in the coil = E × I
= 90 × 23.15
= 2083
Efficiency = 
= 
= 75%
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