Generator Efficiency
Consider an off grid generator is powered by a stationary bicycle. If a volunteer pedals the bicycle with 5 N∙m of mechanical torque at 20 rpm to produce 10 W of electricity, what is the generator’s efficiency?
Expand Hint
Efficiency of a machine:
$$$\eta =\frac{P_{out}}{P_{in}}$$$
where
$$P_{out}$$
is the machine’s output power and
$$P_{in}$$
is the machine’s input power.
Hint 2
Mechanical power in a rotating machine:
$$$P=T \omega_m$$$
where
$$T$$
is the mechanical torque, and
$$w_m$$
is the angular velocity.
Since angular velocity is in rad/s, let’s convert the rotational speed from the problem statement:
$$$\omega_m=\frac{2\pi}{60}n$$$
where
$$n$$
is the speed in rpm.
$$$\omega_m=\frac{2\pi}{60}\cdot 20=2.093\:rad/s$$$
Mechanical power in a rotating machine:
$$$P=T \omega_m$$$
where
$$T$$
is the mechanical torque, and
$$w_m$$
is the angular velocity.
$$$P= (5N\cdot m)(2.093\:rad/s)=10.467\:W$$$
Efficiency of a machine:
$$$\eta =\frac{P_{out}}{P_{in}}$$$
where
$$P_{out}$$
is the machine’s output power and
$$P_{in}$$
is the machine’s input power. For a motor,
$$P_{in}$$
is the active component of the electrical power input, and
$$P_{out}$$
is the mechanical power output. For a generator, it’s vice versa.
$$$\eta =\frac{10W}{10.467W}=0.96$$$
0.96
Time Analysis
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