## 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**

**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**

**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

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Similar Problems from FE Section:

**AC Power**110. Motor Shaft RPM

118. Power Factor

302. Synchronous Speed

397. Induction Motor

401. Motor Slip

405. Motor Poles

499. Torque Units

500. Mechanical Power

501. Sync Speed

502. Machine Efficiency

505. Input Power