---
title: "5-disc string at 66 kV: nearest and farthest disc"
subject: "Power System Analysis I"
chapter: 2
key: "semester_4/power_system_analysis_i:five-discs-66kv-distribution"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/five-discs-66kv-distribution
site: BCT Engineering
---

# 5-disc string at 66 kV: nearest and farthest disc

Power System Analysis I · Chapter 2: Overhead and Underground Transmission

- Asked in: 2068 Bhadra, 5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/five-discs-66kv-distribution
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-2

## Question

There are five discs in a string of insulators used in a 3-phase, 66 kV overhead transmission line. Compute the voltage distribution at the nearest and farthest disc from the phase conductor.

## Short answer

For a 66 kV line (phase voltage 38.1 kV) and five discs with capacitance ratio 0.1, the disc nearest the conductor carries 11.39 kV (29.9% of phase voltage) and the farthest disc carries 5.28 kV (13.9%). The nearest disc is stressed more than twice the farthest.

## Answer

The ratio of shunt to self-capacitance is not given. Assume the usual value $m = C_1/C = 0.1$ (shunt capacitance 10 % of disc capacitance).

#### Data
- Phase voltage: $V = 66/\sqrt3 = 38.105$ kV
- Discs numbered 1 (farthest from the conductor, at the tower) to 5 (nearest the conductor)

#### Relations
$$
V_{k+1} = V_k + m(V_1 + \dots + V_k)
$$

$$
\begin{aligned}
V_2 &= 1.1V_1\\
V_3 &= 1.31V_1\\
V_4 &= 1.651V_1\\
V_5 &= 1.651V_1 + 0.1(5.061V_1) = 2.1571V_1
\end{aligned}
$$

$$
V = 7.2181V_1 \;\Rightarrow\; V_1 = \frac{38.105}{7.2181} = 5.279\ \text{kV}
$$

| Disc | Voltage (kV) | % of $V$ |
|---|---|---|
| 1 (farthest, at tower) | 5.279 | 13.85 % |
| 2 | 5.807 | 15.24 % |
| 3 | 6.916 | 18.15 % |
| 4 | 8.716 | 22.87 % |
| 5 (nearest conductor) | 11.388 | 29.88 % |

String efficiency:

$$
\eta = \frac{38.105}{5\times11.388} = 66.92\ \%
$$

**Answer (with $m = 0.1$):** The disc nearest the conductor carries 11.39 kV (29.9 % of $V$), and the farthest disc carries 5.28 kV (13.9 % of $V$). The nearest disc is stressed more than twice as much as the farthest one.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The ratio m used here (not given in the question) is
   A. 0.01
   B. 0.1
   C. 1
   D. 10
   Answer: B. The usual value m = C1/C = 0.1 is assumed. (Key point: Assumed m)

2. The voltage across the 66 kV string is
   A. 66 kV
   B. 38.105 kV
   C. 114.3 kV
   D. 22 kV
   Answer: B. V = 66/sqrt(3) = 38.105 kV. (Key point: Phase voltage)

3. Which pair of values is correct for the nearest and farthest discs?
   A. 11.39 kV (nearest), 5.28 kV (farthest)
   B. 5.28 kV (nearest), 11.39 kV (farthest)
   C. 7.62 kV each
   D. 13.2 kV (nearest), 5.28 kV (farthest)
   Answer: A. V5 = 2.1571 x 5.279 = 11.388 kV and V1 = 5.279 kV. (Key point: Nearest and farthest discs)

4. The nearest disc is stressed about how much compared with the farthest?
   A. Equally
   B. Slightly more (10 %)
   C. More than twice
   D. Half
   Answer: C. 2.1571 times the farthest disc voltage, which is more than twice. (Key point: Stress ratio)

## Related in Power System Analysis I

- [Voltage distribution on 4-disc string at 33 kV](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Astring-4-discs-33kv) — Power System Analysis I, chapter 2
- [String of 4 insulators at 66 kV, ratio 10](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Astring-4-insulators-66kv-ratio-10) — Power System Analysis I, chapter 2
- [String efficiency: 66 kV, 4 discs, 10%](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Astring-efficiency-66kv-4-discs) — Power System Analysis I, chapter 2, asked 2×
- [5-disc string at 66 kV, ratios 5 and 6](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Astring-efficiency-5-discs-66kv) — Power System Analysis I, chapter 2
- [Line voltage from disc voltages of 4-disc string](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aline-voltage-from-disc-voltages) — Power System Analysis I, chapter 2
- [Maximum voltage of 3-disc string, 17.5 kV per unit](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Amax-voltage-3-disc-17-5kv) — Power System Analysis I, chapter 2

## Related in other subjects

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- [Insulator discs per string, 180 MW over 200 km](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Ainsulator-discs-180mw-200km) — Transmission and Distribution System Design, chapter 3
- [Voltage, circuits, discs: 200 MW, 160 km](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Adesign-200mw-160km-voltage-discs) — Transmission and Distribution System Design, chapter 2
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