## Motor Poles

An induction motor operates with a 0.20 slip, and a line voltage frequency of 120 Hz. If the motor shaft's rotational speed is 11,520 rpm, how many pole(s) does it have?

##
__
__**Hint**

**Hint**

The synchronous speed for ac motors is:

$$$n_s=120*f/p$$$

where
$$f$$
is the line voltage frequency in Hz, and
$$p$$
is the number of poles.

##
__
__**Hint 2**

**Hint 2**

The slip for an induction motor is:

$$$slip=\frac{(n_s-n)}{n_s}$$$

where
$$n$$
is the rotational speed, and
$$n_s$$
is the synchronous speed.

The slip for an induction motor is:

$$$slip=\frac{(n_s-n)}{n_s}$$$

where
$$n$$
is the rotational speed, and
$$n_s$$
is the synchronous speed.

Solving for synchronous speed:

$$$(n_s)slip=n_s-n$$$

$$$n=n_s-(n_s)slip$$$

$$$n=n_s(1-slip)$$$

$$$n_s=\frac{n}{(1-slip)}=\frac{11,520rpm}{1-0.20}=\frac{11,520rpm}{0.80}=14,400\:rpm$$$

The synchronous speed for ac motors is:

$$$n_s=120*f/p$$$

where
$$f$$
is the line voltage frequency in Hz, and
$$p$$
is the number of poles.

Solving for number of poles:

$$$p=\frac{120\cdot f}{n_s}=\frac{120(120)}{14,400rpm}=\frac{14,400}{14,400}=1$$$

1