Given:

• Voltage of disc nearest to conductor V? = V?(1+K), where K is the earth to disc capacitance ratio.
• K = 0.10
• Number of discs n = 5

We can use the formula for string efficiency, which is given by:

String Efficiency = (V? + V? + V? + V? + V?)/(n V?) × 100

where V? is the voltage at the conductor end, V?, V?, V?, and V? are the voltages at the second, third, fourth, and fifth discs respectively, and n is the total number of discs in the string.

Using the given formula V? = V?(1+K), we can find the voltages at each disc as follows:

V? = V?(1+K) = V?(1+0.10) = 1.1V?

V? = V? + (V? + V?)K = 1.1V? + 2.1V?(0.10) = 1.31V?

V? = V? + (V? + V? + V?)K = 1.31V? + 3.41V?(0.10) = 1.651V?

V? = V? + (V? + V? + V? + V?)K = 1.651V? + 5.061V?(0.10) = 2.1571V?

Substituting these values in the formula for string efficiency, we get:

String Efficiency = (V? + V? + V? + V? + V?)/(n V?) × 100

= (V? + 1.1V? + 1.31V? + 1.651V? + 2.1571V?)/(5 × 2.1571V?) × 100

= (7.2181V? / 10.7855V?) × 100

= 66.93 %

Therefore, the string efficiency of the insulator string is 66.93%.