--- title: "Skin effect with AC and DC current" subject: "Power System Analysis I" chapter: 4 key: "semester_4/power_system_analysis_i:skin-effect-ac-dc" source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/skin-effect-ac-dc site: BCT Engineering --- # Skin effect with AC and DC current Power System Analysis I · Chapter 4: Line Parameter Calculations - Asked in: 2082 Kartik (new course), 4 marks - Video: [What is Skin Effect ? Explained | TheElectricalGuy](https://www.youtube.com/watch?v=GnVPc7K_5qY) — Gaurav J - TheElectricalGuy - 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/skin-effect-ac-dc - Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4 ## Question What do you mean by skin effect? Clarify it on the basis of AC current and DC current. ## Short answer Skin effect is the tendency of AC current to concentrate near the conductor surface due to higher internal flux linkage at the center, increasing effective resistance. With DC, current density is uniform and resistance is minimum. With AC, central filaments have higher reactance, pushing current outward, so Rac > Rdc, and the effect grows with frequency and conductor size. ## Answer **Skin effect** is the tendency of **alternating current** to flow mostly near the outer surface ("skin") of a conductor, instead of being spread evenly over its cross-section. #### With DC - The current is steady, so there is no changing flux and no induced emf inside the conductor. - The current divides according to resistance only. Every filament has the same resistance, so the **current density is uniform** over the whole area. - The full area is used, and the resistance is $R_{dc} = \rho l/A$. #### With AC - The changing current produces alternating flux inside the conductor. A filament at the centre is linked by more flux (internal plus external) than a filament at the surface. - So the central filaments have higher inductance and reactance, and larger back-emf. The current is pushed towards the surface, where the impedance is lower. - The effective conducting area is reduced, so $R_{ac} > R_{dc}$. The effect grows with frequency, diameter and permeability. The skin depth is $\delta = \sqrt{2\rho/(\omega\mu)}$, about 9.3 mm for copper at 50 Hz. ```text DC (uniform J) AC (J higher near surface) .-------. .-------. / ::::::: \ / ####### \ | ::::::::: | | ##.....## | | ::::::::: | | #.......# | \ ::::::: / \ ####### / '-------' '-------' ``` | Point | DC | AC | |---|---|---| | Current density | Uniform | Higher at the surface | | Area used | Full area | Reduced effective area | | Resistance | $R_{dc} = \rho l/A$ | $R_{ac} > R_{dc}$ | | Copper loss | $I^2R_{dc}$ | Higher, $I^2R_{ac}$ | | Skin effect | None | Present, rises with f | Effects and remedies: higher losses and lower efficiency. It is reduced by using stranded, ACSR (current flows mainly in the outer aluminium strands), hollow or bundled conductors. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is DC current density uniform over the conductor? A. No changing flux, so current divides by resistance only and every filament has equal resistance B. DC has higher frequency C. DC is attracted to the centre D. Filaments have different inductance Answer: A. Steady current induces no emf, so only resistance matters and it is equal for all filaments. (Key point: DC distribution) 2. Why is AC pushed towards the surface? A. Central filaments link more flux, giving higher reactance and back-emf B. Surface filaments have higher inductance C. AC cannot enter metal D. Resistance is lower at the centre Answer: A. Higher central impedance drives current to the lower-impedance surface. (Key point: AC distribution) 3. How do AC and DC resistances compare and which remedy helps? A. R_ac > R_dc; stranded, hollow or ACSR conductors reduce it B. R_ac < R_dc; solid conductors reduce it C. R_ac = R_dc; no remedy needed D. R_ac > R_dc; increasing frequency reduces it Answer: A. Reduced effective area makes R_ac larger, and stranding, hollow or ACSR conductors lessen the effect. (Key point: Resistance comparison) ## Related in Power System Analysis I - [Skin effect and proximity effect](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Askin-and-proximity-effect) — Power System Analysis I, chapter 4, asked 3× - [Skin effect in transmission lines](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Askin-effect-brief) — Power System Analysis I, chapter 4 - [Ferranti effect and skin effect](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aferranti-and-skin-effect) — Power System Analysis I, chapter 6 - [Why AC prevailed over DC in early 20th century](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aac-prevailed-over-dc) — Power System Analysis I, chapter 1, asked 2× - [Advantages and limitations of DC transmission](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Adc-transmission-advantages-limitations) — Power System Analysis I, chapter 1 ## Related in other subjects - [Feedback effect in DC motor speed control](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Afeedback-dc-motor-speed) — Control Systems, chapter 1 - [Reason: DC series motor on ac supply](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Aseries-motor-ac-supply-reason) — Electrical Machine, chapter 4 - [Shock effects for DC and different AC frequencies](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ashock-effects-dc-ac) — High Voltage Engineering, chapter 2 - [Dielectric power loss under AC and DC](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Adielectric-power-loss-ac-dc) — High Voltage Engineering, chapter 6