Given Information:
Number of turns = N = 84
Area of Rectangular coil = 2.61x3.64 cm = 0.0261x0.0364 m
Magnetic field = B = 0.80 T
Current = I = 10.5 mA = 0.0105 A
Angular speed = ω = 3.54x10³ rev/min
Required Information:
(a) Maximum torque = τmax = ?
(b) Peak output power = Ppeak = ?
(c) Work done = W = ?
(d) Average power = Pavg?
Answer:
(a) Maximum torque = 0.00067 N.m
(b) Peak output power = 0.248 W
(c) Work done = 0.00189 J
(d) Average power = 0.1115 W
Explanation:
(a) The toque τ acting on the rotor is given by,
τ = NIABsin(θ)
Where N is the number of turns, I is the current, A is the area of rectangular coil and B is the magnetic field
A = 0.0261x0.0364
A = 0.00095 m²
The maximum toque τ is achieved when θ = 90°
τmax = NIABsin(90°)
τmax = 84*0.0105*0.00095*0.80*1
τmax = 0.00067 N.m
(b) The peak output power of the motor is given by,
Pmax = τmax*ω
ω = 3.54x10³ x 2π/60
ω = 370.7 rad/sec
Pmax = 0.00067*370.7
Pmax = 0.248 W
(c) The amount of work done by the magnetic field on the rotor in every full revolution is given by
W = 2∫NIABωsin(ωt) dt
W = -2NIABcos(ωt)
Evaluating limits,
W = -2NIABcos(π) - (-2NIABcos(0))
W = 2NIAB + 2NIAB
W = 4NIAB
W = 4*84*0.0105*0.00067*0.80
W = 0.00189 J
(d) Average power of the motor is given by
Pavg = W/t
t = 2π/ω
t = 2π/370.7
t = 0.01694 sec
Pavg = W/t
Pavg = 0.00189/0.01694
Pavg = 0.1115 W
