Why is $3^{rd}$ harmonic dangerous?

Hint: We need to know what the third harmonic is before answering the question. The lowest frequency of a system is called Fundamental frequency, while the higher frequencies are known as Overtones.

Complete answer:
First let us define harmonics. Harmonics are the integral multiple of fundamental frequency or main frequency. It is the positive integer multiple of the fundamental frequencies. In an electric power system, a harmonic of a voltage or current is a sinusoidal wave whose frequency is an integer multiple of the fundamental frequency. These are produced by the action of non-linear loads such as rectifiers.
Now the third harmonic is the third multiple of the fundamental frequency. It is usually called the second overtone in a sound instrument like organ pipes which are used to produce sound by blowing into a pipe.
Now let us examine why the third harmonics are dangerous. Power system harmonics increase the current in the system rapidly. This is particularly correct for the third harmonic. The third harmonic causes a sharp increase in the current in a neutral conductor. Harmonics cause malfunctioning of electronic parts, resulting in transformers heating etc.

Note: It should be noted that all the harmonics are overtones but all overtones are not harmonics. Overtone is a term used to specify any higher standing wave and the term harmonic is used for those cases in which the overtones are integral multiples of the fundamental frequency. The node is a point on the wave where the resultant amplitude is zero while antinodes are those points where the resultant amplitude is maximum. As the number of harmonics increases the wavelength decreases.