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High Voltage Engineering - Over Voltages in Electrical Power Systems - Solved Problems: Over(High) Voltages in Electrical Power Systems

**PROBLEMS**

1. A steady
current of 600 μA flows through the plane electrode separated by a distance of
0.5 cm when a voltage of 10 kV is applied. Determine the Townsend’s first
ionization coefficient if a current of 60 μA flows when the distance of
separation is reduced to 0.1 cm and the field is kept constant at the previous
value.

**Solution: **Since the field is kept constant
(i.e., if distance of separation is reduced, the voltage is** **also reduced by the same ratio so that V/d is kept constant).

I = I_{0}
e^{αx}

Substituting
two different sets of values,

we have
600 = I_{0} e^{0.5α} and 60 = I0 e^{0.1α}

or 10 = e^{0.4α} or 0.4 α = 1n 10

0.4α =
2.3026

α= 5.75
ionizing collisions/cm.

2. The
following table gives two sets of experimental results for studying Townsend’s
mechanism. The field is kept constant in each set:

The
maximum current observed is 6 × 10^{–14} A. Determine the values of
Townsend’s first and second ionization coefficients.

3. The
following observations were made in an experiment for determination of dielectric
strength of transformer oil. Determine the power law equation.

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