# D.C. circuits

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u10-overview/
> Weight: n/a

This unit covers core concepts for analyzing steady-state direct current (DC) circuits, from basic diagram conventions to complex circuit analysis. These concepts underpin all practical and theoretical work on electricity in A-level physics.

**Prerequisites:** [Understanding of basic concepts: current, potential difference, and resistance](https://www.owlsprep.com/study/cie-9702-u09-current-potential-difference-resistance/)

## Learning objectives

- Recall and draw standard DC circuit symbols and interpret circuit diagrams correctly
- Apply Kirchhoff's conservation laws to solve a range of DC circuit problems
- Calculate equivalent resistance for series and parallel resistor combinations
- Analyze potential divider circuits and their practical applications
- Account for internal resistance of real power sources and calculate terminal potential difference

## 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](https://www.owlsprep.com/study/cie-9702-u10-circuit-symbols-and-diagrams/) — Learn standard IEC circuit symbols and how to interpret and draw clear, correct circuit diagrams.
- [Kirchhoff's laws](https://www.owlsprep.com/study/cie-9702-u10-kirchhoff-s-laws/) — Study the two fundamental conservation laws that form the basis of all DC circuit analysis.
- [Series and parallel resistor combinations](https://www.owlsprep.com/study/cie-9702-u10-series-and-parallel-resistor-combinations/) — Apply Kirchhoff's laws to derive and use rules for equivalent resistance of series and parallel networks.
- [Potential divider](https://www.owlsprep.com/study/cie-9702-u10-potential-divider/) — Analyze the common potential divider circuit and its applications in sensors and voltage scaling.
- [Internal resistance](https://www.owlsprep.com/study/cie-9702-u10-internal-resistance/) — Learn to account for the internal resistance of real batteries and calculate terminal potential difference.

## Common pitfalls

- **Wrong:** Treating a battery's e.m.f. as equal to terminal p.d. when internal resistance is non-zero
  - Why it fails: Real batteries always drop potential across their internal resistance when current flows, so terminal p.d. is lower than e.m.f.
  - Correct: Always include internal resistance in your total circuit resistance calculation when current is flowing
- **Wrong:** Mixing up equivalent resistance formulas for series and parallel resistors
  - Why it fails: The reciprocal rule for parallel resistors is often confused with the direct addition rule for series, leading to wrong results
  - Correct: Remember: series resistances add directly, parallel resistances add as reciprocals
- **Wrong:** Ignoring Kirchhoff's laws when using derived combination rules
  - Why it fails: Derived rules for equivalent resistance only work because of Kirchhoff's laws, and do not apply to all circuit configurations
  - Correct: Always verify complex results by checking against Kirchhoff's junction and loop rules

## Cheatsheet

| Concept | Key Formula/Result |
| --- | --- |
| Equivalent resistance (series) | $R_{total} = R_1 + R_2 + ... + R_n$ |
| Equivalent resistance (parallel) | $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}$ |
| Kirchhoff's First Law (junction rule) | $\sum I_{in} = \sum I_{out}$ |
| Kirchhoff's Second Law (loop rule) | $\sum \varepsilon = \sum IR$ around any closed loop |
| Potential divider output voltage | $V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}$ |
| Terminal p.d. with internal resistance | $V = \varepsilon - Ir$ |

## 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.

- [Circuit symbols and diagrams](https://www.owlsprep.com/study/cie-9702-u10-circuit-symbols-and-diagrams/)
- [Kirchhoff's laws](https://www.owlsprep.com/study/cie-9702-u10-kirchhoff-s-laws/)
- [Series and parallel resistor combinations](https://www.owlsprep.com/study/cie-9702-u10-series-and-parallel-resistor-combinations/)

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