---
title: "String efficiency: 33 kV, 3 discs, 10%"
subject: "Power System Analysis I"
chapter: 2
key: "semester_4/power_system_analysis_i:string-efficiency-33kv-3-discs"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/string-efficiency-33kv-3-discs
site: BCT Engineering
---

# String efficiency: 33 kV, 3 discs, 10%

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

- Asked in: 2069 Poush, 6 marks
- Video: [String efficiency problems with solutions | string efficiency numerical problems |Future inventors-1](https://www.youtube.com/watch?v=U_AEQn7GxBA) — Future inventors
- 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/string-efficiency-33kv-3-discs
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-2

## Question

An insulator string for 33 kV overhead line has 3 discs. The shunt capacitance between each joint and metal work is 10% of the capacitance of each disc. Find the voltage across the different discs and string efficiency.

## Short answer

With m = 0.1 and phase voltage 33/√3 = 19.053 kV, disc voltages are 5.59 kV (tower), 6.15 kV, 7.32 kV (line). String efficiency = 19.053/(3×7.319) = 86.77%.

## Answer

#### Data
- Phase voltage: $V = 33/\sqrt3 = 19.053$ kV
- $m = C_1/C = 0.1$
- Discs numbered 1 (tower end) to 3 (line end)

```text
 Tower ─[C]─ A ─[C]─ B ─[C]─ Line (19.05 kV)
             |       |
           0.1C    0.1C  to tower
```

#### Junction A
$$
\omega CV_2 = \omega CV_1 + \omega(0.1C)V_1 \;\Rightarrow\; V_2 = 1.1V_1
$$

#### Junction B
$$
V_3 = V_2 + 0.1(V_1 + V_2) = 1.1V_1 + 0.21V_1 = 1.31V_1
$$

#### Disc voltages
$$
V = V_1(1 + 1.1 + 1.31) = 3.41V_1 \;\Rightarrow\; V_1 = \frac{19.053}{3.41} = 5.587\ \text{kV}
$$

| Disc | Voltage (kV) | % of $V$ |
|---|---|---|
| 1 (tower end) | 5.587 | 29.33 % |
| 2 | 6.146 | 32.26 % |
| 3 (line end) | 7.319 | 38.42 % |

#### String efficiency
$$
\eta = \frac{V}{3V_3} = \frac{19.053}{3\times 7.319} = 86.77\ \%
$$

**Answer:** The disc voltages are 5.59 kV, 6.15 kV and 7.32 kV, and the string efficiency is 86.77 %.

## Check yourself

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

1. The shunt capacitance being 10 % of each disc's capacitance gives
   A. m = 10
   B. m = 0.1
   C. m = 0.9
   D. m = 1.1
   Answer: B. m = C1/C = 0.1. (Key point: Meaning of 10 %)

2. V3 in terms of V1 is
   A. 1.1 V1
   B. 1.21 V1
   C. 1.31 V1
   D. 1.41 V1
   Answer: C. V3 = V2 + 0.1(V1+V2) = 1.1V1 + 0.21V1 = 1.31 V1. (Key point: Junction B)

3. The line-end disc voltage is
   A. 5.59 kV
   B. 6.15 kV
   C. 7.32 kV
   D. 19.05 kV
   Answer: C. V1 = 19.053/3.41 = 5.587 kV and V3 = 1.31 x 5.587 = 7.319 kV. (Key point: Disc voltages)

4. String efficiency is
   A. V/(3 V3) = 86.77 %
   B. 3V3/V = 115 %
   C. V1/V3 = 76 %
   D. V/V3 = 260 %
   Answer: A. eta = 19.053/(3 x 7.319) = 86.77 %. (Key point: Efficiency)

## Close variants set in other exams

- [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×

## 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
- [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
- [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
- [Voltage across string discs is not uniform](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Astring-voltage-not-uniform) — Power System Analysis I, chapter 2, asked 3×
- [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: 3 units, 25% and 10%, 25 kV](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Astring-efficiency-3-unit-25kv) — Power System Analysis I, chapter 2, asked 2×

## Related in other subjects

- [Number of insulator discs for 220 kV line](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Ainsulator-discs-220kv-appendix) — Transmission and Distribution System Design, chapter 3
- [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
- [Tower top potential and insulator string voltage](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Atower-top-potential-insulator-voltage) — High Voltage Engineering, chapter 3, asked 2×