For a transmission system of voltage ‘765 kV’ volts having the core radius of ‘5’ cm and outer radius of ‘0.40’ m. The maximum dielectric stress on single-core cable is _________.a)7357.7kVb)919.7kVc)4247kVd)530kVCorrect answer is option 'A'. Can you explain this answer?

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Answer

The maximum dielectric stress on a single-core cable can be calculated using the equation:

$E_{max} = \frac{V}{\ln(\frac{r2}{r1})}$

Where:
$E_{max}$ is the maximum dielectric stress
$V$ is the voltage of the transmission system
$r1$ is the inner radius of the cable
$r2$ is the outer radius of the cable

Given:
Voltage (V) = 765 kV
Inner radius (r1) = 5 cm
Outer radius (r2) = 0.40 m

Converting the inner radius to meters:
$r1 = 0.05$ m

Substituting the values into the equation:

$E_{max} = \frac{765 \times 10^3}{\ln(\frac{0.40}{0.05})}$

Simplifying the equation:

$E_{max} = \frac{765 \times 10^3}{\ln(8)}$

Using the natural logarithm of 8:

$E_{max} = \frac{765 \times 10^3}{2.0794}$

Calculating the value:

$E_{max} \approx 7357.7$ kV

Therefore, the maximum dielectric stress on the single-core cable is approximately 7357.7 kV.

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