---
title: "Resultant of two alternating currents"
subject: "Basic Electrical Engineering"
chapter: 5
key: "semester_1/basic_electrical_engineering:resultant-current-two-sinusoids"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/resultant-current-two-sinusoids
site: BCT Engineering
---

# Resultant of two alternating currents

Basic Electrical Engineering · Chapter 5: Alternating Quantities

- Asked in: 2074 Asoj, 4 marks
- Video: [Electrical Engineering: Ch 10 Alternating Voltages & Phasors (7 of 82) Adding Sinusoidal Functions](https://www.youtube.com/watch?v=wE8IMkYG0EI) — Michel van Biezen
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/resultant-current-two-sinusoids
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-5

## Question

Two alternating currents represented by the equations i1 = 7sinωt and i2 = 10sin(ωt + π/2) are fed into a common conductor. Find the equation for the resultant current and its RMS value.

## Short answer

Adding phasors: I1=7∠0° A, I2=10∠90° A gives resultant peak magnitude √(7²+10²)=12.21 A at angle 55.0°. Resultant current equation: i=12.21 sin(ωt+55.0°) A. RMS value: 12.21/√2=8.63 A.

## Answer

Given i₁ = 7 sin ωt and i₂ = 10 sin(ωt + π/2) = 10 cos ωt.

#### Phasor addition (peak values)

- I₁ = 7∠0° = 7 + j0
- I₂ = 10∠90° = 0 + j10
- I = I₁ + I₂ = 7 + j10

Magnitude: Im = √(7² + 10²) = √149 = 12.21 A

Phase angle: φ = tan⁻¹(10/7) = 55.0° = 0.960 rad

**Resultant current: i = 12.21 sin(ωt + 55.0°) A**

#### RMS value

I_rms = Im / √2 = 12.21 / 1.4142 = **8.63 A**

Check: I₁rms = 4.95 A, I₂rms = 7.07 A, and √(4.95² + 7.07²) = 8.63 A (the two currents are in quadrature).

## Check yourself

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

1. i2 = 10 sin(wt + pi/2) equals?
   A. 10 sin wt
   B. 10 cos wt
   C. -10 cos wt
   D. 10 sin 2wt
   Answer: B. A 90 degree shift. (Key point: Conversion)

2. Peak resultant?
   A. 8.63 A
   B. 3 A
   C. sqrt(149) = 12.21 A
   D. 17 A
   Answer: C. Quadrature. (Key point: Magnitude)

3. RMS value?
   A. 12.21 A
   B. 8.63 A
   C. 17 A
   D. 6.2 A
   Answer: B. Im/sqrt2. (Key point: RMS)

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