---
title: "Laplace: current supplied by source, 10 V"
subject: "Electrical Circuit Theory"
chapter: 4
key: "semester_3/electrical_circuit_theory:laplace-source-current-10v-1ohm-1h"
source: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/laplace-source-current-10v-1ohm-1h
site: BCT Engineering
---

# Laplace: current supplied by source, 10 V

Electrical Circuit Theory · Chapter 4: Transient analysis in RLC circuit by Laplace Transform

- Asked in: 2067 Asar (old course), 8 marks
- Video: [Introductory Circuit Analysis: Laplace Transform](https://www.youtube.com/watch?v=WHhPFsFUxz8) — STEM Trek
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/laplace-source-current-10v-1ohm-1h
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_circuit_theory/chapter-4

## Question

In the network shown, the switch is closed at t = 0. Find the current supplied by the source using Laplace transform method.
[Figure: 10 V source with a switch (t = 0) feeding two parallel branches: a 1 Ω resistor in series with a 1 H inductor, and a 2 Ω resistor in series with a ½ F capacitor]

## Short answer

Find branch currents: I1(s)=10/[s(s+1)], I2(s)=5/(s+1). Summing, I(s)=10/s −5/(s+1). Inverse transform gives source current i(t)=10 −5e^(−t) A, t≥0.

## Answer

Zero initial conditions (switch closes at t = 0). The source is 10/s. Branch impedances: Z₁ = 1 + s (R = 1 Ω, L = 1 H) and Z₂ = 2 + 2/s (R = 2 Ω, C = ½ F).

#### Branch currents
```text
I1(s) = (10/s) / (1 + s)
I2(s) = (10/s) / (2 + 2/s) = 5 / (s + 1)
```

#### Source current
```text
I(s) = I1 + I2 = 10/[s (s + 1)] + 5/(s + 1)
     = 10/s − 10/(s + 1) + 5/(s + 1)
     = 10/s − 5/(s + 1)
```
(equivalent to I = V/Z_eq = 5(s + 2)/[s(s + 1)])

**i(t) = 10 − 5e^(−t) A, t ≥ 0**

Individual branches: i₁ = 10(1 − e^(−t)) A and i₂ = 5e^(−t) A.

Check: i(0⁺) = 0 + 10/2 = 5 A (L open, C short) ✓; i(∞) = 10/1 = 10 A (C open, L short) ✓.

## Check yourself

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

1. What are Z1 and Z2?
   A. Z1 = 1 + s and Z2 = 2 + 2/s
   B. Z1 = 1 + 1/s and Z2 = 2 + s/2
   C. Z1 = 1 + s and Z2 = 2 + s/2
   D. Z1 = s and Z2 = 2/s
   Answer: A. RL: R + sL; RC with C = 1/2: R + 1/(sC) = 2 + 2/s. (Key point: Branch impedances)

2. What is I2(s) and i2(t)?
   A. 10/(s+1); i2 = 10 e^(-t)
   B. 5/(s+1); i2 = 5 e^(-t)
   C. 5/s; i2 = 5
   D. 5/(s+2); i2 = 5 e^(-2t)
   Answer: B. (10/s)/(2 + 2/s) = 10/(2(s+1)) = 5/(s+1). (Key point: Branch current 2)

3. What is i(t) and its limits?
   A. 10 + 5 e^(-t); 15 A at 0+
   B. 10 - 5 e^(-t); 0 at 0+
   C. 10 - 5 e^(-t); 5 A at 0+ and 10 A at infinity
   D. 5 e^(-t); 5 A at 0+ and 0 at infinity
   Answer: C. At 0+ L is open and C short so i = 10/2 = 5 A; at DC C is open and L short so i = 10/1 = 10 A. (Key point: Source current)

## Related in Electrical Circuit Theory

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## Related in other subjects

- [Source current by series-parallel reduction](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aseries-parallel-current-30v-r1-r9) — Basic Electrical Engineering, chapter 2