---
title: "KCL, KVL and types of sources"
subject: "Basic Electrical and Electronics Engineering"
chapter: 1
key: "semester_1/basic_electrical_and_electronics_engineering:kcl-kvl-sources"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_and_electronics_engineering/kcl-kvl-sources
site: BCT Engineering
---

# KCL, KVL and types of sources

Basic Electrical and Electronics Engineering · Chapter 1: Fundamentals of Electrical and Electronics Circuits

- Asked in: 2081 Chaitra (new course), 2+4 marks
- Video: [KVL and KCL (Circuits for Beginners #11)](https://www.youtube.com/watch?v=f2iCGcWShLE) — Aaron Danner
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_and_electronics_engineering/kcl-kvl-sources
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_and_electronics_engineering/chapter-1

## Question

State KCL and KVL. Explain different types of voltage and current sources.

## Short answer

KCL: algebraic sum of currents at a node is zero. KVL: algebraic sum of voltages around a loop is zero. An ideal voltage source maintains constant terminal voltage regardless of load; a practical source has internal series resistance. An ideal current source supplies constant current irrespective of terminal voltage; a practical source has internal parallel resistance.

## Answer

#### Kirchhoff's laws

**KCL (current law):** the algebraic sum of the currents meeting at a node is zero. Equivalently, current entering a node equals current leaving it: $\sum I=0$. It follows from conservation of charge.

**KVL (voltage law):** the algebraic sum of all voltages (sources and drops) around any closed loop is zero: $\sum V=0$. It follows from conservation of energy.

#### Voltage and current sources

An **ideal voltage source** keeps a fixed terminal voltage whatever the load current; its internal resistance is zero. A **practical voltage source** is an ideal source $E$ in series with an internal resistance $r$, so $V=E-Ir$ and the terminal voltage falls with load.

An **ideal current source** supplies a fixed current whatever the load voltage; its internal resistance is infinite. A **practical current source** is an ideal source $I_s$ in parallel with an internal resistance $r$.

| Type | Description |
|---|---|
| Independent source | Value fixed, unaffected by any other circuit quantity (battery, generator) |
| Dependent (controlled) source | Value depends on a voltage or current elsewhere in the circuit (VCVS, CCVS, VCCS, CCCS), as in transistor models |
| DC source | Constant polarity, e.g. cell, battery |
| AC source | Alternating polarity, e.g. alternator |

**Source conversion.** A practical voltage source $E$ with series $r$ is equivalent to a current source $I_s=E/r$ with the same $r$ in parallel, which simplifies network analysis.

## Check yourself

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

1. KCL states that the algebraic sum of currents at a node is zero. Which principle does it express?
   A. Conservation of charge
   B. Conservation of energy
   C. Faraday's law
   D. Maximum power transfer
   Answer: A. Charge cannot accumulate at a node, so current in equals current out. (Key point: KCL basis)

2. KVL states that, around any closed loop, the algebraic sum of source voltages and drops is zero. Which principle does it follow from?
   A. Conservation of charge
   B. Lenz's law
   C. Conservation of energy
   D. Ohm's law
   Answer: C. Energy gained from sources equals energy lost in drops around a closed loop. (Key point: KVL)

3. Which pairing of source and internal resistance is correct?
   A. Ideal voltage source: infinite resistance
   B. Ideal current source: zero resistance
   C. Practical voltage source: ideal source E in series with r, V = E - Ir
   D. Practical current source: ideal source in series with r
   Answer: C. A practical voltage source is E in series with r so terminal voltage falls with load; ideal voltage source has r = 0, ideal current source r = infinity, and a practical current source has r in parallel. (Key point: Ideal vs practical sources)

4. How is a practical voltage source E with series resistance r converted?
   A. Current source Is = E x r with r in series
   B. Current source Is = E/r with the same r in parallel
   C. Current source Is = E/r with r in series
   D. Voltage source of E/r with r in parallel
   Answer: B. The equivalent is a current source Is = E/r with the same r in parallel. (Key point: Source conversion)

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