Unit Overview

D.C. circuits

CIE A-Level Physics· 5 min read 📊 n/a

1. Unit at a glance

This unit follows a progressive learning path, starting from core conventions to practical circuit analysis. We begin with standard diagram conventions, the universal language of circuit work. Next we introduce the fundamental conservation laws that govern all DC circuits, then apply these laws to common resistor combinations, before covering two widely used practical circuit concepts: potential dividers and internal resistance of real power sources.

Work through these sub-topics in order to build your understanding:

Circuit symbols and diagrams

Learn standard IEC circuit symbols and how to interpret and draw clear, correct circuit diagrams.

★⏱ 3 min

Kirchhoff's laws

Study the two fundamental conservation laws that form the basis of all DC circuit analysis.

★★★⏱ 4 min

Series and parallel resistor combinations

Apply Kirchhoff's laws to derive and use rules for equivalent resistance of series and parallel networks.

★★⏱ 4 min

Potential divider

Analyze the common potential divider circuit and its applications in sensors and voltage scaling.

★★★⏱ 5 min

Internal resistance

Learn to account for the internal resistance of real batteries and calculate terminal potential difference.

★★★⏱ 4 min

2. Common Pitfalls

Wrong move:

Treating a battery's e.m.f. as equal to terminal p.d. when internal resistance is non-zero

Why:

Real batteries always drop potential across their internal resistance when current flows, so terminal p.d. is lower than e.m.f.

Correct move:

Always include internal resistance in your total circuit resistance calculation when current is flowing

Wrong move:

Mixing up equivalent resistance formulas for series and parallel resistors

Why:

The reciprocal rule for parallel resistors is often confused with the direct addition rule for series, leading to wrong results

Correct move:

Remember: series resistances add directly, parallel resistances add as reciprocals

Wrong move:

Ignoring Kirchhoff's laws when using derived combination rules

Why:

Derived rules for equivalent resistance only work because of Kirchhoff's laws, and do not apply to all circuit configurations

Correct move:

Always verify complex results by checking against Kirchhoff's junction and loop rules

3. Quick Reference Cheatsheet

Concept	Key Formula/Result
Equivalent resistance (series)	$R_{t o t a l} = R_{1} + R_{2} + ... + R_{n}$
Equivalent resistance (parallel)	$\frac{1}{R _{t o t a l}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + ... + \frac{1}{R _{n}}$
Kirchhoff's First Law (junction rule)	$\sum I_{in} = \sum I_{o u t}$
Kirchhoff's Second Law (loop rule)	$\sum ε = \sum I R$ around any closed loop
Potential divider output voltage	$V_{o u t} = V_{in} \times \frac{R _{2}}{R _{1} + R _{2}}$
Terminal p.d. with internal resistance	$V = ε - I r$

What's Next

Start with the first sub-topic below to review core circuit conventions, the essential starting point for all further circuit analysis. Work through each sub-topic in order, as each concept builds directly on the previous one. Once you complete all sub-topics in this unit, you will move on to study alternating current circuits, which extend the DC concepts you learn here.