---
title: "Initial values of all currents and voltages at t=0+"
subject: "Electrical Circuit Theory"
chapter: 2
key: "semester_3/electrical_circuit_theory:initial-values-many-quantities-10v-2ohm"
source: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/initial-values-many-quantities-10v-2ohm
site: BCT Engineering
---

# Initial values of all currents and voltages at t=0+

Electrical Circuit Theory · Chapter 2: Initial Conditions

- Asked in: 2068 Shrawan, 8 marks
- Video: [Initial Conditions in R, RL & RC Circuits Made Easy | t=0⁺ Explained in Simple Way || EC Academy](https://www.youtube.com/watch?v=5wuJCsKDIBg) — EC Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/initial-values-many-quantities-10v-2ohm
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_circuit_theory/chapter-2

## Question

The switch has been open for a long time in the circuit shown below and at t = 0 it is suddenly closed. Find iL, vC, qC, i2Ω, i3Ω, i1Ω, iC, vL, v3Ω, v1Ω, v2Ω at t = 0⁺.
[Figure: 10 V source in series with a 2 Ω resistor that has a switch (t = 0) connected in parallel across it. After that, two parallel branches: a 3 Ω resistor in series with a 4 H inductor, and a 2 F capacitor in series with a 1 Ω resistor.]

## Short answer

iL = 2 A, vC = 6 V, qC = 12 C; i3Ω = 2 A, v3Ω = 6 V; i1Ω = iC = 4 A, v1Ω = 4 V; vL = 4 V; i2Ω = 0, v2Ω = 0.

## Answer

**Circuit:** 10 V source in series with 2 Ω, which has a switch connected across it. Then two parallel branches: 3 Ω + 4 H, and 2 F + 1 Ω. The switch has been open for a long time and closes at t = 0.

#### At t = 0⁻ (steady state: L short, C open)

```text
i_L = 10/(2 + 3) = 2 A
v_C = voltage across the 3 Ω resistor = 3 × 2 = 6 V (no current in the C branch)
```

#### At t = 0⁺

The inductor current and capacitor voltage are continuous. The closed switch shorts the 2 Ω resistor, so the full 10 V is across the two parallel branches.

| Quantity | Value at 0⁺ | Working |
|---|---|---|
| i_L | 2 A | continuity |
| v_C | 6 V | continuity |
| q_C | 12 C | C·v_C = 2 × 6 |
| i₃Ω | 2 A | same as i_L |
| v₃Ω | 6 V | 3 × 2 |
| v_L | 4 V | 10 − 6 |
| i₁Ω | 4 A | (10 − 6)/1 |
| i_C | 4 A | same as i₁Ω |
| v₁Ω | 4 V | 1 × 4 |
| v₂Ω | 0 V | shorted by the switch |
| i₂Ω | 0 A | no current in the resistor (6 A flows through the switch) |

Check: source current = 2 + 4 = 6 A, all through the switch.

**Answer: i_L = 2 A, v_C = 6 V, q_C = 12 C, i₃Ω = 2 A, v₃Ω = 6 V, i₁Ω = i_C = 4 A, v₁Ω = 4 V, v_L = 4 V, i₂Ω = 0, v₂Ω = 0.**

## Check yourself

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

1. What are i_L and v_C at t = 0−?
   A. i_L = 2 A, v_C = 6 V
   B. i_L = 5 A, v_C = 0
   C. i_L = 2 A, v_C = 10 V
   D. i_L = 0, v_C = 6 V
   Answer: A. 10/(2 + 3) = 2 A and 3 × 2 = 6 V. (Key point: Steady-state)

2. What is v_L at 0+?
   A. 10 V
   B. 10 − 6 = 4 V
   C. 6 V
   D. 0
   Answer: B. Full 10 V is across the branch and 3 Ω drops 6 V. (Key point: Inductor voltage)

3. What is i1Ω = i_C?
   A. 6 A
   B. 10 A
   C. 4 A
   D. 2 A
   Answer: C. (10 − 6)/1. (Key point: 1 Ω branch)

4. What is the 2 Ω resistor current and voltage at 0+?
   A. 5 A, 10 V
   B. 2 A, 4 V
   C. 6 A, 12 V
   D. 0 A and 0 V
   Answer: D. It is shorted by the switch. (Key point: 2 Ω)

## Close variants set in other exams

- [Initial values with 20 Ω shorted by switch, 4 H, 2 F](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Ainitial-values-switch-open-20-30) — Electrical Circuit Theory, chapter 2, asked 2×

## Related in Electrical Circuit Theory

- [Initial currents i1, i2, i3 at t=0+ with C1, C2, L](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Ainitial-values-three-loop-currents-v) — Electrical Circuit Theory, chapter 2
- [Initial values with switch open to closed (10 Ω, 15 Ω, 2 F)](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Ainitial-conditions-switch-open-10-15) — Electrical Circuit Theory, chapter 2
- [Laplace: iL(t) and vc(t) after switch opens](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Alaplace-il-vc-48v-5ohm-switch) — Electrical Circuit Theory, chapter 4
- [Laplace: currents i1 and i2 with L and C branches](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Alaplace-currents-i1-i2-100v-r1) — Electrical Circuit Theory, chapter 4
- [Show i1 = i2 = -V/(R1+R2+R3) at t=0+](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Aswitch-a-to-b-initial-values) — Electrical Circuit Theory, chapter 2
- [Classical: i1, i2 with two R-L branches](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Aclassical-i1-i2-100v-10ohm-1h) — Electrical Circuit Theory, chapter 3

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